Diffraction problems with Loudspeaker Enclosures:

Can Diffraction problems in loudspeaker enclosures be solved by a combination of careful electronics engineering and careful aiming of loudspeaker drivers to eliminate diffraction effects? 

The short answer is NO.  But Why ?

The reason for this answer is bandwidth.  Loudspeakers operate normally between 20 hz and 20,000 hz.

Corrections using either electronics to compensate for diffraction, the baffle-step, aiming drivers, etc. are at best a very crude attempt to adjust the 19,800 individual frequencies that loudspeakers need to properly reproduce.  The corrections also are diffracted when they pass by edges and/or bounce around like a delay-line inside a loudspeaker enclosure.  

Simulations of the diffraction effect inside and outside any loudspeaker enclosure require the computing power of a weather forecasting model like the ETA, UKMET, RUC, GBL, NOGAPS model ensembles.  Huge supercomputers using chaos theory in conjunction with standard hydrodynamic theory in a 3-D atmospheric view in time-slices are used by the models cited.  Any loudspeaker engineering that does not use real-time models for each of the 19,800 frequencies that incorporate both inside the enclosure, time-delayed bounce through the driver, enclosure vibration, outside enclosure shape effects and the interactions between all the elements simply can not properly reduce diffraction-effects like a simple curved loudspeaker enclosure using materials that equal the loudspeaker enclosure.

The tested answer is to use curved loudspeaker enclosures that naturally work to eliminate both internal and external diffraction effects.  The enclosure shapes are mass-manufacturable, are made of materials that are engineered specifically for loudspeaker enclosure applications, have a wide variety of class A finishes, and are consumer-acceptable for a given application due to elastic design ability.


Using electronics would require giving a supercomputer with each loudspeaker enclosure to model and adjust all 19,800 separate "channels" on a true real-time basis to match what curved enclosures automatically do.  The output of a loudspeaker enclosure that uses carefully adjusted driver positions still has the problem of the output passing over diffracting elements and neither method addresses the chaos which occurs inside the loudspeaker enclosure even with a 60 db absorption which still pushes against the drivers  


THIS IS HOW CABINET SHAPE AFFECTS THE SOUND YOU HEAR. Notice how only one shape, the sphere, has the smoothest response. You can see how all other shapes introduce increased distortion. Yet loudspeaker companies continue to mount speakers in boxes. This experiment was performed by Harry F. Olson, EE, PhD, Director of the Acoustical Research Laboratories for RCA at Princeton.

Dr. Olson then presented the paper in 1950. This effect has been published for 60 Years. Olsen's references go back to 1938 as found in our technical paper. It is our hope that this century will be a more enlightened one, particularly in regard to loudspeaker design, fabrication, and marketing.


WHAT HAPPENS WHEN SOUND HITS AN OBJECT. For example, when soundwaves from a speaker strike the cabinet walls  of the speaker. Notice how the sphere is the shape which offers the least cabinet distortion. 

Sphere shapes have been hung in certain amphitheaters to improve and correct the sound.

74  JULY - AUG 2001
by IIpo Martikainen
& Nick Zacharov   


One of the important phenomena affecting sound radiation of a loudspeaker is diffraction. Explained simply this means that any edges, for example the loudspeaker cabinet edges, act as secondary sound sources. As the cabinet front panel usually has four edges, the system has five radiators operating at the same time, the actual driver and four secondary sources. The resulting frequency response at the listening position is the sum of all these sources.  The summed frequency response varies because of the summing of components with different arrival times. As the listener moves off-axis, the relative distances of the secondary sources change. The summed response heard at the listening position is different due to the secondary radiations.  The existence of secondary sources degrades the response of a loudspeaker. On-axis there is ripple due to the summing of coincident edge diffractions. Off-axis the summing is no longer coincident as the path lengths are different, which results in lower amplitude of ripple spread more evenly over frequency. This is usually seen at and above midrange frequencies due to the physical dimensions of loudspeaker compared to the wavelength of the radiated sound. A reduction in sound level occurs when the difference of the direct radiation path and the path length of  the diffracted sound equals half the wave length ((l))
b + c - a = l/2 .  Loudspeaker cabinet diffraction has been carefully studied in acoustical textbooks (Muller et al. (1938) and Olson (1947)). The box shape and the driver location are key factors.

Effects of diffraction
To reduce the frequency response ripple the distances from the driver to cabinet edges can be made unequal so that the ripple pattern is distributed more evenly over frequency. Off-axis the frequency responses of left and right speakers will then differ blurring the stereo image. To avoid this many speakers of this type are built in mirror pairs. A very useful and simple test of stereo performance is to use a mono signal. The centre image should be sharp at all frequencies. Reproduction of a mono signal is a simple way to check the system’s ability to reproduce phantom images in general. If the mono image is wide and frequency dependent, then the stereo performance is usually also bad. Diffraction is not the only reason for poor mono performance, but include other reasons are beyond the scope of this article.

Loudspeaker Diffraction Distortion and Radiation Impedance

By Bohdan Raczynski


Diffraction distortion ( or diffraction loss ) appears to be one of those subjects, that easily attract a number of "pro" and "against" arguments. When considering a typical domestic listening environment, where some sound reflections are inevitable anyway, one may stop to ponder - should I make a big fuss about it or not. There are a few facts to consider first. (1) Even a medium size front baffle (60cm x 60cm) produces diffraction distortion in order of +9dB at 400Hz (accordingly to Olson [62]).

This is well within woofer operating frequency range for 2-way and 3-way systems. The diffraction loss is the easiest to observe in the anechoic chamber, but it exists in most situations where the speakers are not radiating into half-space. (2) Contemporary dome midrange and tweeter drivers are specifically designed to have wide radiation angle (omnidirectional) and therefore be prone to diffraction distortion. Diffraction effect will typically add +6dB at higher frequencies for asymmetrically mounted drivers. (3) Many currently available loudspeaker systems are placed sufficiently far away from the walls of the listening room to be subjected to diffraction distortion of varying degree. (4) Listening rooms of today are being acoustically treated for the best balance of the direct and reflected sound.

This may be even unintentional, as simply having a carpet, drapes and some soft furniture in the room. In fact, Christensen [2] for example, develops several useful rules for improving listening pleasure in typical room, with the emphasis on reducing 1-st reflections. Therefore, typical listening environment is nowhere near the "reverberant room", which reflects all the sound produced inside it and makes the diffraction distortion difficult to separate. Finally, there is the issue of consistency in the design approach. Here is one point of view. It is known, that room modal response at low frequencies (standing waves) causes 30dB variations in the low end of the frequency response of the loudspeaker, but this has NOT deterred anybody from using technically sound approach (Small/Thiele parameters) for proper design of the enclosure.


Why should this approach be limited only to the low end of the audio spectrum ?. In the mid to high frequency range room reflections will also distort the frequency response of the loudspeakers, so should the design methodology be relaxed and the diffraction distortion neglected in this frequency range ?. We would advocate careful consideration of the "whole picture". At least as long as loudspeakers are tested and compared in anechoic chambers and placed away from the walls in well designed listening rooms. You see, at some point of the design process, you need to gain the confidence, that you are creating the best source of

Diffraction distortion

Loudspeaker diffraction loss has been studied and discussed by engineers and researchers extensively over the years. Available test results support the scientific findings and several models have been proposed to adequately quantify the phenomenon. Current discussions revolve around selecting the fastest and most accurate algorithm modeling the phenomenon on currently available computer hardware. Plainly speaking, when testing in the anechoic chamber, at high frequencies the speaker is radiating into "half space" (2p) i.e. it is only radiating into the forward hemisphere. At low frequencies the speaker radiates into "full space", (4p) exhibiting a loss of bass when implemented in typical speaker enclosures. The difference in the SPL is 6dB and is referred to as the "6 dB baffle step" or the enclosure’s "diffraction loss". The location of the "baffle step" on the frequency scale is dependent on the dimensions of the baffle. The smaller the baffle the higher the transition frequency. Diffraction Loss modeling performed for this article is based on the GTD (Geometric Theory of Diffraction). Figure 1 below explains basic idea of GTD. The loudspeaker is mounted on a baffle and it generates certain SPL level at the "Observer" location. The observer receives a combination of direct (A) rays and diffracted (B) rays.

Figure 1. GTD concept.


Loudspeaker enclosure or baffle and the placement of the driver contribute up to +10dB to the frequency response of the system. The GTD using ray model is applied to determine the exact amount of SPL deviation due to the diffraction. In this model, sound rays, B, propagate along the surface of the baffle and are scattered when encounter the edge of the baffle. This secondary sources combine with the direct rays, A, produced by the loudspeaker and the resulting frequency response is far from being flat. To calculate the contribution of baffle edge, total length of the baffle edge is quantized into a number of sections of length dx. The average distance from each section to the "point source" representing the loudspeaker is rk. If dx is made sufficiently small, it can be replaced with a "diffraction point source".


Figure 2. Single driver diffraction

Knowing the SPL of each "diffraction point source" and the distance to the observer, it is possible to predict the total SPL from the driver and all of the diffraction sources. I have selected 48 dx line elements to represent top and bottom edge of the baffle and 96 dx line elements to represent the left and right side of the baffle. Loudspeaker driver is modeled as 8 "point sources" contributing to the direct SPL. For the purpose of modeling the diffraction loss, I also assume, the reference distance to the observer to be the standard 1 meter. This situation is depicted on Figure 2. You can also change loudspeaker location on the front baffle, the dimensions of the baffle and microphone distance. Asymmetrical mounting of the loudspeaker will result in "smoother" frequency response. The enclosure diffraction effect is much less pronounced when the test microphone is placed much closer to the loudspeaker. The distance that can be preset the "direct" sound (ray A) has to travel is only 1cm, but the "diffracted" (ray B) wave has to travel to the edge of the enclosure and back, therefore it will arrive at the test microphone at much lower level. This situation is depicted on Figure 3. Here, the level picked up by the microphone is much higher due to close proximity to the speaker, and at the same time, the ripples due to enclosure diffraction are almost non-existent.


What does this mean for you at home situation ?. One possible approach to modeling and testing loudspeakers is using 2p (half-space) approach advocated by LMS "pit measurement" technique to obtain frequency response of all drivers used in the system. This is good approach and guarantees, that all drivers (including woofer) radiate into half space, so their respected SPL levels are +6dB over the 4p technique. This is not a problem, as loudspeaker modeling software facilitates shifting the SPL curves up or down.

Figure 3. Near-field diffraction


However, if the system design is based on those measurements and tested in anechoic chamber, the diffraction distortion will manifest itself quite clearly. Now the system radiates into 4p space and the enclosure diffraction loss comes into play producing relative loss of bass below certain frequency determined by the enclosure geometry. The tweeter will continue to see 2p radiating space thanks to the enclosure diffraction. A simple solution to this problem, that has been around for some time, is to pre-distort the frequency response of the woofer crossover to account for the enclosure loss (or gain to be more precise) and attenuate tweeter accordingly.


Mutual Radiation Impedance

When two loudspeakers are mounted on the same baffle and fed the same signal, one driver starts to produce additional pressure on the other, increasing its radiation impedance. The next logical step is therefore to determine power radiated by two sources mounted on the same baffle. Vanderkooy and Lipshitz [3] examined a simple case of two pistons mounted in an infinite baffle and proposed an elegant formula for expressing radiated power into the farfield taking into account self and mutual radiation impedance of source1 (piston1) coming from itself and from piston 2. 

For low frequencies, the above result is four times (or 6dB SPL) the single source result. Factor k, plotted for single driver vs. frequency (Figure 4) exhibits 3dB raise at low end of the spectrum and 0dB at the high end of the frequency range. For two drivers, the curve is up by 3dB and it can be observed, that 3dB gain in SPL is attributed to doubling the electrical power supplied to two drivers connected in parallel. Additional 3dB gain in SPL is due to mutual radiation impedance effect. Engebretson in [4] indicated, that this additional increase in effciency will hold to a frequency above which the diaphragms no longer "couple". This phenomenon has been experimentally verified by Gander and Eargle in [5]. They have performed comparative measurements on single subwoofer loudspeaker vs. an array of 8 subwoofers noting increase in SPL at 30Hz as 21dB. Of this gain, they attributed 9dB to 8-fold increase in input power (8 = 2x2x2 = 3dB+3dB+3dB) and 9dB to mutual coupling increasing 3dB per doubling of units. Additional 3dB gain was due to slight increase in directivity index of this large array. Also, Keele [6], investigating the performance of Bessel Arrays concluded that an array of two loudspeakers simply connected in-parallel, exhibits maximum SPL increase of 6dB, but only up to a frequency where the sources are about 1/4 wavelength apart.


Signal Summation Strategies

Power Summation and Phasor Summation strategies have been the two main methods used in prediction programs. The Power Summation method assumes, that phase interaction between arriving signals can be ignored and only mean square pressures are added. Using this convention, the SPL of two equal signals would increase by 3dB. Summation example for N identical sources p, is shown below. 

The Power Summation technique will sometimes produce different result from the Phasor Summation technique. However, it works well in the case of mutual radiation impedance, because the drivers, are closely coupled and are driven from the same source (amplifier), so they can be considered coherent (radiating signal with same phase). Therefore, the SPL increase is the same (+6dB) as would be if the Phasor Summation method was used. This assumption holds only up to certain frequency and is dependent on the geometry of the system.

The Phasor Summation method computes the phase and magnitude of each arriving signal and sums them as vectors (complex addition). Using this technique, the predicted SPL for two equal signals will by 6dB greater than the SPL produced by single source. Again, summation example for N sources p, driven by a common signal is shown below. The Phasor Summation technique was used in calculating diffraction from the enclosure edges. As you may recall, we specifically looked at each signal's path length and added all arrivals as vectors.


Combining All the Above

We are now in good position to review the SPL gains due to:

1. enclosure diffraction,

2. mutual radiation impedance and

3. multiple drivers in the same enclosure.

We assume that: (1) our amplifier is an ideal voltage source - this is the case of most currently available amplifiers. The amplifier will deliver 10VRMS to the load. (2) all drivers are identical and have real impedance of 4ohm. For the input voltage of 10VRMS, the loudspeaker will deliver 100dB SPL. Finally, (3) for the purpose of evaluating SPL levels for different combination of drivers, we will keep the amplifier output constant (no change in volume level). The 0.0dB reference level shown on following figures corresponds to 100dB SPL.


Single driver.

This is our reference case. The amplifier will deliver 25W electrical power to the speaker (U*U/R = 10*10/4 = 25 W) and the loudspeaker will now generate 100dB SPL. The diffraction effect will add +6dB in the upper end of the operating frequency range and the SPL gains curve will look as on Figure 2. Being the ideal voltage source, the amplifier will also cope well with the 8ohm load impedance being now presented to it ( two 4ohm loudspeakers connected in-series). Each driver will now receive only half of the 10VRMS voltage generated by the amplifier. 

With this in mind, each speaker will receive only 6.25W of electrical power ( U*U/R = 5*5/4 = 6.25 W ) Each driver will now generate only 94dB SPL, so that total SPL of the system is now 97dB. The diffraction effect will add +6dB in the upper end of the operating frequency range and the mutual radiation impedance effect will add +3dB in the lower end of the operating frequency range. The final SPL gains curve is shown on Figure 2. The electrical power delivered to the system is now only a quarter (12.5W) of the single driver configuration.


Two drivers connected in-parallel.

Being the ideal voltage source, the amplifier will cope well with the 2ohm load impedance being now presented to it ( two 4ohm loudspeakers connected in-parallel). Each driver will generate 100dB SPL, so that total SPL of the system is now 103dB. The diffraction effect will add on the top of it +6dB in the upper end of the operating frequency range and the mutual radiation impedance effect will add +3dB in the lower end of the operating frequency range. The final SPL gains curve is shown on Figure 4. It is worth noticing, that electrical power delivered to the system is now twice (50W) of the single driver configuration.

Figure 4. Two drivers connected in-parallel


Two drivers connected in-series.

Each driver will now receive only half of the 10VRMS voltage generated by the amplifier. With this in mind, each speaker will receive only 6.25W of electrical power ( U*U/R = 5*5/4 = 6.25 W ) Each driver will now generate only 94dB SPL, so that total SPL of the system is now 97dB. The diffraction effect will add +6dB in the upper end of the operating frequency range and the mutual radiation impedance effect will add +3dB in the lower end of the operating frequency range. The electrical power delivered to the system is now only a quarter (12.5W) of the single driver configuration.


Four drivers connected in-series and in-parallel.

This type of configuration results in the system input impedance equal to that of single driver (4ohm). Therefore the electrical power delivered to the system is now 25W. The SPL gains curve can now be constructed from two SPL levels representing drivers connected in-series (the whole curve will raise by +3dB) and again, the mutual radiation impedance effect, which will add +3dB in the lower end of the operating frequency range. The final SPL gains curve is shown on Figure 5. In the lower end of the frequency range, the SPL level is +6dB over the single driver configuration and in the high end the levels are identical (also +6dB). Each driver receives only 6.25W of electrical power, which is 1/4 of the single driver configuration. 

However, combination of all three factors mentioned before, produces fairly bumpy +6dB SPL gain from the "quad box". Figure 5. Four drivers connected in-series and in-parallel - Quad Box



[1]. Harry F. Olson, "Direct Radiator Loudspeaker Enclosures", Audio Engineering, November, 1951.

[2]. Ole Lund Christensen, "A practical guide to acoustical design of control rooms and placement of

loudspeakers", Copenhagen AES Convention 1989, Also available from

http://Ampspeaker.com/guide_to_design.html .

[3]. J. Vanderkooy and S.P. Lipshitz, "Power Response of Loudspeakers with Noncoincident Drivers - The

Influence of Crossover Design", 74th Convention of the AES, New York, 1983.

[4]. M. E. Engebretson, "Low-Frequency Sound Reproduction", JAES, Vol 32, May 1984.

[5]. M.R. Gander and J.M.Eargle, "Measurement and Estimation of Large Loudspeaker Array Performance",

JAES, Vol 38, April 1990.

[6] D.B. Keele, "Effective Performance of Bessel Arrays", JAES, Vol 38, October 1990.

Loudspeaker Diffraction Loss
and Compensation
John L. Murphy
Physicist/Audio Engineer


Loudspeaker enclosure "diffraction loss" occurs in the low frequency range of loudspeakers in enclosures that are located in the open, away from walls or other surfaces. The essence of it is this: At high frequencies the speaker is radiating into "half space" i.e. it is only radiating into the forward hemisphere. No significant energy is radiated to the rear of the speaker. At low frequencies the speaker is radiating into both the forward hemisphere and the rear hemisphere. That is, at low frequencies the speaker radiates into "full space". Because the "energy density" at low frequencies is reduced there is a loss of bass. In short, speaker systems designed for radiation into half space (mounted flush on an infinite plane) exhibit a loss of bass when implemented in typical speaker enclosures. Fortunately, this bass loss can be accurately modeled and subsequently compensated.

Most loudspeaker modeling is performed based on the assumption of radiation into half space. A speaker radiating into half space plays 6 dB louder than the same speaker radiating into full space. This is the crux of the diffraction loss. A full range speaker finds itself radiating into half space at the upper frequencies but radiating into full space at lower frequencies. As a result, there is a gradual shift of -6dB from the highs to the lows. This is what is called the "6 dB baffle step" or the enclosure’s "diffraction loss". The center frequency of the transition is dependent on the dimensions of the baffle. The smaller the baffle the higher the transition frequency. 

The shape of the diffraction loss frequency response curve depends on the size and shape of the enclosure. Olson has carefully documented the diffraction loss of enclosures of various shapes (see references below). All enclosure shapes exhibit a basic 6 dB transition (or "step") in the response with the bass ending up 6 dB below the treble. A spherical enclosure exhibits this transition clearly with a very smooth diffraction loss curve. In the curves below I have taken the liberty of extending the frequency range of Olson's original graphs from 100 Hz to 20 Hz at the low end and from 4kHz to 5 kHz at the high end. The low frequency response was extended to more clearly reveal the "stepped" nature of the response. I wanted it to be clear that the response levels off at the low end. Olson's own reproductions of the measured diffraction loss of a sphere by Muller, Black, and Davis tend to confirm that my extensions to the responses are correct.

Diffraction Loss of a

More "angular" enclosures exhibit the underlying 6 dB step along with a series of response ripples that are dependent on the placement of the speaker with respect to the baffle edges. The worst case appears to be placing the driver at the center of a circular baffle so that it is the same distance from all diffracting edges.

Diffraction Loss of a


Diffraction Loss of a Cube

Placing the driver on the baffle so that it is a different distance from each edge tends to minimize the response ripples and make the diffraction loss look more like the smooth loss of the sphere. Olson's rectangular enclosure is an improvement over the cube and the cylinder face but the driver is still equidistant from three edges. Other authors report further reduction in the ripples with careful driver placement and edge rounding.

Diffraction Loss of a
                                        Rectangular Enclosure

Because the spherical diffraction loss is a common element for the diffraction of all enclosures and the response ripples are much more difficult to predict (and can be minimized anyway) it makes sense to approximate the diffraction loss of a loudspeaker as the diffraction loss of the equivalent sphere.

One simple electrical circuit which produces a 6 dB step reduction in the bass response is shown below.

If we let R1 = R2 = R then a 6 dB attenuation results at low frequencies. At higher frequencies (where C1 becomes a low impedance) the attenuator is effectively bypassed and the signal is passed without attenuation.

It can be shown that the 3 dB "center" frequency for the above network is given by:

The frequency response of diffraction modeling network typically looks like this:

Careful inspection of Olson's spherical diffraction loss curve reveals a -3dB frequency of about 190 Hz for the 24" sphere. Assuming that the 3 dB frequency is inversely proportional to the baffle diameter I have arrived at the following approximation for calculating the -3dB frequency as a function of baffle diameter.

f(3) = 115/W(B)
(where W(B) is the baffle width in meters)


f(3) = 380/W(B)
(where W(B) is the baffle width in feet)

Sanity Check: for Olson's 24" (2 feet) baffle we calculate f(3) = 380/2 = 190 Hz . . .OK!

Once the diffraction loss is known it is possible to design a simple electrical network that will exactly mirror the spherical diffraction loss and restore the lost bass to a speaker system. Loudspeaker designers have traditionally compensated for the diffraction loss by reducing the level of the tweeter and making other adjustments in the crossover. The method I propose is to design for half space but then do a precise mirror image compensation for the diffraction loss by way of an R-L network wired in series with the (impedance compensated) speaker. Alternately, the diffraction loss can be compensated at line level with a simple R-R-C network. Line level correction would reduce the requirement for the large inductors typically needed for a speaker level compensation network.

A simple electrical network which produces a 6 dB step reduction in the treble response is shown below.

Here R2 represents the loudspeaker load impedance. If we let R1 = R2 = R then a 6 dB attenuation results at high frequencies. At lower frequencies (where L1 becomes a low impedance) the attenuator is effectively bypassed and the signal is passed to the driver (R2 here) without attenuation.

The frequency response of 6 dB diffraction compensation network looks like this:

To design an RL network which will compensate for diffraction loss of a particular system we start by setting:

R1 = R2 = R =Nominal System Impedance (8 Ohms for example)

Next, you can use my empirically derived equation to calculate the value of the inductor L1:

Where W(B) is the baffle width in meters, R is in Ohms, and L1 in millihenrys.

I arrived at this equation for L1 by forcing the 3 dB frequency of the compensating network to match the 3 dB frequency for the diffraction loss of the baffle.

The resulting RL network should be wired in series with the speaker system it is compensating. The correction will be most accurate if the loudspeaker itself approximates a resistive load.


Find the network required to compensate the spherical diffraction loss of a 4 Ohm speaker system with a 0.25 meter wide baffle.

R = 4 (the nominal impedance of the system)
(this resistor should have a power rating something like a quarter of the system power rating)

L1 = .25 x 4 / 1.021 = 1 / 1.021

L1 = .979 mH
(1 mH will be close enough)

To build this network, start by connecting a 4 Ohm resistor in parallel with a 1 mH inductor. Then connect this RL network in series with the speaker. You should hear reduced treble when the diffraction loss compensator is used.

WinSpeakerz models the diffraction loss of the enclosure as a simple spherical diffraction loss. Provided the driver is located "irregularly" on the baffle this gives very good approximation to the actual diffraction loss of the enclosure. The frequency of the transition is controlled by the "Baffle Width" parameter at the System Editor page 1. The response of the speaker can be viewed with or without the diffraction loss and the diffraction loss can also be viewed separately.


25Jun99 A follow-up post on this topic:


> I've been researching the idea of adding a baffle step compensation circuit
> to my Marchand XM9 active crossover.  The only thing that seems hard to do
> is calculate the amount of boost actually needed as this is room dependent. 
> The theory, see John Murphy's article at http://www.trueaudio.com/, suggests 6db
> boost.  An article at the TL web page suggests 3db is more likely with room
> reinforcement.  Has anyone looked at this. 

The 6 dB loss is correct for a speaker enclosure in free space.  When the enclosure is placed in a room it will encounter various effects due to the room (reverb, standing waves, boundary effect, cavity effect . . .) 

Diffraction loss and room effects are independent and completely different effects.  The diffraction loss is nicely predictable whereas the effects of the room are highly variable, not only from room to room but also with speaker placement and room furnishing.  This typically means that each listening environment will be unique and will require unique compensation.

I suggest the 6 dB diffraction loss correction as a correction for the diffraction loss alone.  I don't suggest that it will neutralize all the effects due to a unique listening environment.  Others suggest you "deal with diffraction" in the crossover, usually by just lowering the tweeter level a bit.

In some situations  3 or 4 dB of diffraction loss correction may result in an overall response that is closer to neutral (flat).  But the most correct way to compensate the room would be to do it separately from any diffraction loss correction.  Room compensation might take the form of several notch filters tuned to the worst peaks resulting from room modes.  Next you might want to tilt the treble up a smidge to compensate for reverberation that has significant treble loss.  Dark room reverb will make the playback sound a little darker. Bright reverb . . .  bright.  Next, depending on the size of the room and speaker response, you might need to compensate for the cavity effect.  In larger rooms cavity effect can be ignored but in vehicle cabins it is a major effect. 

Diffraction loss compensation is only part of the job of precisely compensating for the difference between a theoretical half-space acoustic load and what happens when we place an enclosure in a real world listening room.  Reducing the degree of diffraction loss compensation MAY reduce the coloration from the room effects as these effects largely tend to "boost the bass" but such an adjustment is imprecise at best. 

If we can systematically identify each source of color between our half space model and our particular listening room then we can then take steps to precisely neutralize the response in our own listening room.  Spherical diffraction compensation is one effect we can correct with a high degree of precision.  As we move toward a better understanding and modeling of our listening rooms I'm sure we will work out more practical and precise ways to compensate our rooms. 

Comments and critique are welcome.      :-)



John L. Murphy
Physicist/Audio Engineer
True Audio
Check out my new book "Introduction to Loudspeaker Design" at Amazon.com



Loudspeaker Diffraction Technical References

Revised: 20Jun00

Wright, J. R.
"Fundamentals of Diffraction"
Journal of the Audio Engineering Society
Vol. 45, No. 5, 1997 May, pp.347-356

NOTE:  The above reference was published after this tech topic was completed and thus was not included in the original list of references.  I would suggest that this be the first reference studied by anyone beginning an investigation into loudspeaker diffraction phenomena.  In particular, note that Wright questions the validity of certain details in some of these previous papers, especially regarding the phase change of the diffracted wave. Some of the previous papers incorrectly indicated that there was no phase difference between incident and diffracted waves in the illuminated zone.  jlm  20Jun00

Rasmussen, Soren and Rasmussen, Karsten Bo
"On Loudspeaker Cabinet Diffraction"
Journal of the Audio Engineering Society
Vol. 42, No. 3, 1994 March, pp.147-150
(for comments on the above article see: Verification of Vanderkooy’s "Simple Theory".
JAES, Vol. 42, No. 10, 1994 October, p.826)

Vanderkooy, John
"A Simple Theory of Cabinet Edge Diffraction"
Journal of the Audio Engineering Society A modification of GTD.
Vol. 39, No. 12, 1991 December, pp.923-933

Gonzalez, Ralph E.
"A Dual-Baffle Loudspeaker Enclosure for Balanced Reverberant Response"
Audio Engineering Society Preprint No. 3203
Presented at the 91st AES Convention, Oct 1991

Porter, James, and Geddes, Earl
"Loudspeaker Cabinet Edge Diffraction"
Journal of the Audio Engineering Society
Vol. 37, No. 11, 1989 November, pp.908-918

Backman, Juha
"Computation of Diffraction for Loudspeaker Enclosures"
Journal of the Audio Engineering Society
Vol. 37, No. 5, 1989 May, pp.353-362

Bews, R. M., and Hawksford, M. J.
"Application of Geometric Theory of Diffraction (GTD) to
Diffraction at the Edges of Loudspeaker Baffles"
Journal of the Audio Engineering Society
Vol. 34, No. 10, 1986 October, pp.771-779

Kral, Robert C.
"Diffraction - the True Story"
Speaker Builder Magazine, 1/80, pp.28-33

Olson, H. F.
"Direct Radiator Loudspeaker Enclosures"
Journal of the Audio Engineering Society
Vol. 17, No. 1, 1969 October, pp.22-29

Muller, G.G., Black, R., and Davis, T. E.
"The Diffraction Produced by Cylindrical and Cubical Obstacles
and by Circular and Square Plates"
Journal of the Acoustical Society of America
Vol. 10, No. 1 (July 1938), pp. 6-13


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The Three Main Problems


In the 1940's and 50's radio and then television irrevocably associated speakers with boxes. Rectangular enclosures are, unfortunately, the consumer-accepted ideal of what a speaker should come in.

However, by 1939, research done by Harry F. Olson, Director of Acoustic Research for the RCA laboratories at Princeton proved conclusively that the sphere is simply the best shape for an audio enclosure. (Ref. 10)

But first let us start with the basic engineering. There are three basic problems in loudspeaker engineering: (Ref. 8).

Phase cancellation

This means that the waves coming out of the front of the speaker should never be allowed to meet the waves coming out of the back of the speaker. The back wave can and will attenuate or distort the front wave if given a chance.


Solid bodies have a frequency of resonance. For example, this is why virtually all speaker boxes are made with particle board, which is composed of different size and shape wood particles compressed and glued together. The different particles all have different frequencies of resonance. Thus, the overall frequency of resonance is close to zero.

But if the challenge is to get good sound in a small space, vented designs may be the most practical alternative. If so, the enclosure should be anti-resonant, but the space of the enclosure and the port should be resonant with the resonant frequency of the speaker.

Radiation resistance

The ambient surroundings have a resistance to being pushed and pulled by the speaker. Air itself has a resistance to being pushed and pulled. Any leak or hole in the enclosure will present resistance, as will any cloth or obstruction in the path of the sound. The question is a matter of what degree. We can assume the enclosure is airtight and any grill or cloth covering the speaker presents minimal resistance. If so, then this problem is essentially solved by proper placement of the speakers.

Now let us re-examine these problems in light of the fact spheres are the best enclosure. How do we get the ultimate sound using the perfect shape enclosure?

Phase cancellation

Today, the mounting frames of most speakers are gasketed to the outside of the enclosure, and the reason for this is to minimize phase cancellation. Although bass reflex ports offer increased efficiency by utilizing the back wave, they can present some distortion because of phase cancellation in certain configurations and frequencies, and would not be used in a design for the very best sound. At low frequencies, the waves will try to wrap around the back. This is another reason why the sphere is the best shape. Waves wrapping around a sphere simply roll off the back. Waves wrapping around any other shape will diffract and distort.


What kind of materials should be used? We have found through experimentation that highly rigid, amorphous materials are best. Amorphous glass meets these requirements and is cost-effective as well, although polymer concrete may also serve. In particular, the material comprising the sphere should be sealed together in several different-size-and-shape pieces using a rubbery glue such as RTV silicone, thus yielding a very anti-resonant and acoustically inert enclosure.

If size is a constraint, often the only practical alternative is to use a port design. The volume of the enclosure is dictated by the wave mapping procedure set out below. From there, it is necessary to know the resonant frequency of the speaker. The resonant frequency of the enclosure can be found by successive approximation. I use a custom-designed spreadsheet and enter different port hole or duct tube diameters until I match the resonant frequency of the speaker within the desired number of decimal places.

The resonant frequency of a ported or ducted enclosure is: Fr= 1/2pi sq root MC

where M is the inertance of the port and CA is the acoustic capacitance of the enclosure.(Refs 4,1) This should be as close as possible to the resonant frequency of the speaker, which is measured using an AC voltmeter and an audio oscillator or signal generator.


Radiation resistance

As mentioned before, good placement is the simplest way of dealing with this problem. Generally we recommend that our speakers be placed slightly away from the wall so they have "room to breathe". The corners of a room are usually the best places for speakers. In fact, if placed in a corner, facing parallel to a wall, the speaker will produce images on the other wall and the floor, which forms a three-sided "horn" loaded by the two images and the speaker. Bass ports are also aided by corners. This has the effect of extending the apparent size of the room. (Ref 5). If at all possible, a properly matched two-speaker rear channel is recommended for extra realism. Thus, four corners will completely load an average room.



Room Acoustics Fundamentals
Basics of nodes and standing waves...
By Bob Ross

NOTE:  when the author says "Room", think CABINET--

Getting your music room to sound good can be a confounding and frustrating experience if you don’t take some basic physics into consideration. There are some fundamental principles of acoustics that apply to all small rooms with parallel walls. Once you are aware of the behavior of sound waves in these spaces, it becomes much easier to understand why music sounds the way it does when played in a certain room. It also can help predict how music will sound in that room, and how this “room sound” might affect your recordings

Two terms, which you will invariably encounter in any discussion of studio acoustics, are Room Modes and Standing Waves. The two terms are very closely related, practically synonymous. Moreover, they are inextricably related to the physical dimensions of your room.

A room mode is essentially a resonance, an area of increased amplitude that results when a sound wave reflects off a boundary surface (wall, floor, or ceiling) and combines in phase with the original direct sound wave. What causes the direct and reflected waves to combine in phase is simply a whole-number correlation between the length of the sound wave and the length (or width, or height) of the room.

Sound waves are variations in air pressure, alternating plus or minus the static atmospheric pressure of a given space. (Here’s a thought experiment: what’s the difference between variations in barometric pressure – i.e., the weather – and really, really low bass notes? Talk amongst yourselves.) The amount by which it exceeds (plus or minus) the static atmospheric pressure is the amplitude of the wave (which corresponds to the Sound Pressure Level).

Antinodes and nodes

Areas of maximum amplitude, representing the maximum change in air pressure, are called Antinodes. Areas of minimum change in air pressure (essentially the zero-crossings between positive and negative halves of the pressure wave cycle) are called Nodes. The concept of nodes may be familiar to string instrument players: Natural harmonics, those pure tones that are played by lightly stopping a string at some fraction of its length, occur at the node of that vibrating string length.

If a sound wave is exactly one-half the length of any single room dimension, its nodes will be at that boundary surface [Fig. 1]. The reflection off of that parallel surface will be in phase with the initial sound wave, the antinodes will line up in space/time and reinforce one another, and there will be an increase in amplitude at that fundamental frequency.

This phenomenon not only occurs for frequencies whose wavelength is one-half a room dimension; it also occurs at any whole number multiples of that frequency…i.e., harmonics of that fundamental.

Double that fundamental frequency and a full wave cycle now fits in the space between boundaries [Fig. 2]. The nodes will still occur at the room boundaries, causing the reflections to be in phase. However, there is now an additional node in the middle of the room; the antinodes of the harmonics do not line up physically with the location of the fundamental’s antinodes. This has important consequences, as we shall see.

Standing waves

These sound waves whose wavelength is equal to one-half (or any whole number multiple of) a room dimension, and hence whose nodes occur at boundary surfaces, are called Standing Waves. Actually, they’re a very specific type of standing wave: Axial Mode is the name given to standing waves that exist between two parallel surfaces (front and back walls, left and right side walls, or floor and ceiling). Other types of standing waves include the Tangential Mode, where the sound wave bounces off of four distinct surfaces, and the Oblique Mode, where all six room boundaries are involved.

Since axial modes are the most troublesome standing waves in music studios, they are our primary concern. Incidentally, they are called standing waves because unlike most sound waves in an enclosed space, axial modes do not propagate through the room. Rather, they occupy a stationary location in that room, their amplitude peaks always occurring at a particular (and predictable) physical location in the space.

How to measure and calculate

To calculate the axial modes of a rectangular room, one uses the formula

1130 / 2L = f

1130 is the approximate speed of sound in feet per second, and L represents the length of a room dimension in feet. The result f is the frequency of the axial mode in Hertz. So for example, if your control room has an 8-foot ceiling...

1130 divided by (2 times 8), or

1130 divided by 16

equals 70.625

...there will be a standing wave (between floor and ceiling) at 70.6 Hz. There will also be a standing wave at the whole number multiples of 70.6, including 141.2 Hz (70.6 x 2), 211.8 Hz (70.6 x 3), 282.4 Hz (70.6 x 4), and so on.

For any rectangular room, there will be a standing wave at each of the three fundamental axial modes (corresponding to the room’s length, width, and height) as well as at the whole number multiples of those three frequencies.

This, in recording studio parlance, sucks.

Bad news

Picture this: There is a standing wave between your 8-foot ceiling and floor at 70.6 Hz. This means the antinode of this fundamental will be equidistant between the floor and ceiling. So there’s an area of maximum amplitude four feet off the ground…right about ear level when you’re sitting in front of the console.

There’s also a standing wave at 141.2 Hz, only because a complete wave cycle fits between those room boundaries, the node (area of least amplitude) of that wave is four feet off the ground. Regardless of what type of monitor speakers you use, or where in the room they are placed, your perception of 70.6 Hz and 141.2 Hz will be colored by the existence of these standing waves. Move your head to another place in the room (e.g., stand up) and the response at 70.6 Hz and 141.2 Hz is different, because now instead of sitting in the antinode and node of those respective waves, you’re in a place where they have a different amplitude relationship. No wonder it’s hard to fit that kick drum into the mix reliably.

And this is only the effect of the first two axial modes of one dimension we’re talking about! Imagine what happens when you add in a third axial mode. Now imagine what happens when you add in axial modes from the other two dimensions. Wait, don’t imagine it; calculate it.

Calculate the fundamental axial modes for each of the three dimensions of your room using the formula 1130 / 2L = f. Multiply each of those three frequencies by 2 through 8 to figure out the first eight multiples of each axial mode. (We’re only concerned with the first eight multiples because above 300–400 Hz, standing waves have less of a destructive influence on sound.)

You should wind up with a list (or a table, or a graph, if you’re industrious) of 24 frequencies. Yep, there’s a standing wave at each one of those frequencies. But don’t panic yet. If they’re fairly evenly spread out, you got lucky, and you should put down this magazine and go make some music now! However…if any of those standing waves are within 5 Hz of each other, these will be problem areas in your room’s frequency response.

My particular room

The control room I used when writing this article was 12' x 10' x 8'. Plotting the axial modes indicated potential problems around 141 Hz (the second multiple of the 8' dimension is 141.3, and the third multiple of the 12' dimension is 141.2…for all practical purposes those numbers are identical). It also pointed to the likelihood of serious problems at 282.5 Hz: the fourth multiple of the 8' dimension, the sixth multiple of the 12' dimension, and the fifth multiple of the 10' dimension all come to exactly that number!

So what can you do about standing waves? Here’s what won’t help: Sticking foam, or fiberglass, or heavy drapes on the walls. Remember that standing waves occur as a result of the physical dimensions of the room. To a 141 Hz sound wave (whose wavelength happens to be eight feet long), a few inches of fuzz on the wall is essentially invisible. If you want to alter the standing waves in your room, you have to change the dimensions of the room. That’s right…knock a wall down, and move it closer or farther away. That’s the only way to change where the standing waves will occur.

Forewarned is forearmed

This is why it’s a good idea to plot the axial modes of a room before you decide to turn it into your recording studio; if you’ve got a choice between several rooms, choose the one whose dimensions yield the more evenly spaced axial modes. (Hint: Try to stay away from rooms where any two dimensions are multiples of one another, and avoid perfectly cubical rooms at all costs. Plot the axial modes and you’ll see why.) And if you’re planning on building any walls (say, to separate your control room from your recording space), calculate the axial modes to determine what the best dimensions for those spaces will be. And if possible, angle walls so they’re not parallel, which can help break up those modes.

That’s not to say there’s nothing you can do to improve the sound of a room already plagued by standing waves…but that’ll have to wait for another article!

What makes the design so revolutionary? The first thing you notice about the Ultimate acoustic enclosure is the shape. In 1950, H. F. Olson, Director of Acoustic Research for RCA Laboratories, Princeton conclusively proved the sphere is the best shape for an audio enclosure. (Ref. 10). Furthermore, sound scientists have known since 1938 that the sphere offers the smoothest response to sound (Ref. 11).

The second thing you notice are the materials. We use only amorphous, anti-resonant, high-stiffness, acoustically inert materials in our enclosures. Thus, vibration, noise, and distortion are all dramatically reduced or even eliminated.

Finally, the design and construction of the speaker enclosures uses a unique approach. Our approach combines proven principles (Refs 5,6,7) with cutting-edge scientific knowledge obtained from our own experiments. We use a proprietary "wave-mapping" procedure to model a design on a computer. Bass-port enclosures are designed using several software packages, to double and triple-check acoustic action. The enclosures are constructed as a series of one-piece spherical layers, so there are no joints in the structure. We also try to take into account the actual environment in which the speakers will be placed.(Ref. 3) For example, we made a pair of speakers for an apartment situation where the left side has not only the door (which may be open or closed) but a pathway into the kitchen to fill as well. Our solution was to seal the right speaker (which is in a smooth corner) into a stone-textured(black granite) sphere, then we gave the left speaker a crystal-clear ball with dual 1-inch diameter port tubes, angled to fill both the door, the kitchen, and match up with the other speaker facing into the living room. The result was a pair of speakers that really make a statement, both sonically and visually.

How much extra does it cost the manufacturer? Costs are equal or lower than the manufacture of current enclosure designs. The design is well-suited for mass manufacturing.

Why does it work? The enclosure is designed using fundamental and applied principles of physics and engineering (Refs 1,4). Our wave-mapping procedure and bass-port design algorithm was inspired by and draws upon wave mechanics physics(Refs 8,9). The enclosure materials are amorphous, thus they are anti-resonant all the way down to the molecular level. High-stiffness materials reduce vibration. Laminating composite materials makes the enclosure both airtight and strong.

Both the interior and exterior shape, materials, and construction assist the driver or drivers to deliver the ultimate sound it is capable of. To quote Tappan (Ref 12) "A wall that is curved in one or both dimensions is more rigid perpendicular to its surface than a flat wall...The improvement of a wall with reasonable curvature over a flat one is so great that a curved panel of thin cardboard is frequently acoustically adequate".

What are the test results? We took a $17 Radio Shack speaker and put it into enclosures with identical interior volume. Both tests were run in the same room, in the same location, in the same position. Both speakers were sealed into the enclosure. Both enclosures are lined with long-staple fiberfill for back-wave damping. The only difference between the enclosures is shape, materials, and construction.

The tests were conducted using a Super Omni microphone and a series of computer-generated test tones at 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 15360, and 17920 Hz. The microphone and test tones were run through separate amplifiers to avoid crosstalk or feedback. The microphone was suspended from the speaker face center axis at a distance of approximately 18 inches. Response from each tone was measured three times for accuracy and the most stable or average value was recorded.

Free Software:  Called CircFFT, it is a circular FFT display, or spectrum the musical way.
Free Software:  Directionality Simulation called Xdir.
Free Software:  TimDec is a program that measures the reverberation time of rooms. TimDec measures the decay time by playing bursts (typically 1 s long) of noise through a loudspeaker, and record it with a microphone. During the burst a diffuse field will build up in the room, and when the noise is turned off, the diffuse field will decay. TimDec chops the recorded signal into windows, which are run through a fast fourier transform (FFT). TimDec plays and records several cycles of this noise burst and calculates an average, in order to achieve smooth graphs of the reverberation.  The loudspeaker should preferably, but not necessarily be omnidirectional. If it is not, it should be directed away from the microphone. The microphone should be omnidirectional, and placed far away from the loudspeaker and typically not next to a wall.


Harry F. Olson, EE, Ph.D, Acoustical Research Dir., RCA labs, Princeton ©1947, D. Van Nostrand Co., Inc., NY

2. "The Home Experimenter's Guide to Multi Channel Listening"
Ralph Hodges, Stereo Review, October 1971, pp.62-64

R. D. Ford, ©1970, Elsevier Pub. Co. Ltd., NY

Abraham B. Cohen, Engr. Mgr., Univ. Loudpeakers, Inc. ©1956, John F. Rider Pub. Inc., NY

Martin Colloms, ©1985, Pentech Press, London

Howard M. Tremaine, ©1959, Howard W. Sams, Indianapolis

Roger R. Sanders, ©1995, Audio Amateur Press, Peterborough, N.H.

By Nikola Tesla with additional material by David Hatcher Childress ©1993, Adventures Unlimited Press, Illinois

10. "Direct Radiator Loudspeaker Enclosures"
Harry F. Olson, Audio Engineering, November 1951, an AES paper presented October 27, 1950

11. Muller, Black, and Dunn, Jour. Acous. Soc. Amer., Vol 10, No. 1, p.6, 1938

12. "Loudspeaker Enclosure Walls"
Peter W. Tappan, Jour. Audio Engr. Soc, Vol 10, No. 3, July 1962