# Help understanding sound wave interference from two sources as a function of distance and frequency

I am trying to optimize the acoustics of a room in my house for music listening. I use a computer that runs a free app called, REW (room Equalization Wizard) . This app can play a test noise through my speakers and simaltaneously record the resulting output and echoes through a calibrated microphone attached to one of its USB ports. I did some measurements and am getting some weird resonances. The speakers are 72" apart and the distance to the microphone is 72" as well (an equilateral triangle). The frequency vs loudness graph looks like this: When I move the microphone 2 inches to the right so that the distance to the left speaker is 73" and the distance to the right speaker is 71 inches the frequency sweep looks like this moving the microphone again so it is 4 inches to right of center results in and moving it to 6 inches to the right of center gives

A 4 inch wavelength sound wave has a frequency of 3376 hertz. Maximum destructive interference would occur at difference of 2 inches from one speaker to the other and this is seen in the second turquoise graph.There is a dip at the expected region of 3400 hertz. But why are there dips at 11k and 18k as well? The wavelength at 11k is 1.29" and the wavelength at 18k is .75"

And when the microphone is moved to 4 inches to right of center, I measured the distance to the left speaker at 74" and the distance to the right speaker is 70". The expected positive reinforcement at 3.4k is actually seen at 3k And there are again multiple other peaks.

Moving the microphone 6" to the right results in 75" to L speaker and 69" to R speaker.

Can some explain why I get such a regularly distributed array of interference peaks across the frequency spectrum?

To rule out artifacts from the speakers I measured the frequency response of each speaker alone and the result was an almost flat curve (Revel ultima Salon2 speakers). To rule out artifacts from the signal processing chain, I reproduced these results using a mac laptop and sending the signal to different DAC. The space where this is being done has sound absorbing material on the walls (heavy curtains). The distance from the speakers to the back wall is 72" and the distance from each speaker to its respective side wall is 45".

After some help from the folks at sound.stackexchange, it seems the phenomenon I stumbled across is comb filtering. The result of two copies of a sound arriving at a location with a time delay between them. My understanding as interference was correct.

You are ignoring reflections from your room. That is what is causing the low frequency "comb" pattern in your first equilateral-triangle experiment.

Even if you have heavy drapes covering the walls, you probably still have strong reflections from the ceiling, and maybe from the floor as well.

If you can move the test set up out of doors, you should get results that correspond to your theory. A grass lawn makes a very good non-reflective "floor", and you should be able to avoid other reflections from buildings, fences, etc.

Obviously, there is too little information in your post to attempt to model the effects of the floor and ceiling - e.g. we don't know the height of the room and the height of the speakers and microphone above the floor, or the directional response of your speakers and mike.

You might consider measuring the impulse response of the room with the sound source at each speaker location (separately) and the various microphone positions, rather than trying to calculate what is happening from first principles.

• thank you for your reply. The room is 13 feet wide and 45 feet long. A screen separates the room into two areas. The listening area is heavily carpeted everywhere. The ceiling is canted with the right wall at 7 feet high and the left at 15. There is a double doorway on the left that opens to another room so no reflections can come from this wall. The microphone is at the height of the tweeters. The combing pattern also occurs when I move the microphone to the left. If reflections were an issue, the asymmetry of the room would prevent the symmetrical appearance of the combing pattern. Commented Aug 13, 2020 at 0:31
• An image of the room is here i.imgur.com/P1OCFRA.jpg Commented Aug 13, 2020 at 0:34
• Since high frequencies are extremely directional, reflections would not play as much a role in the strong interference at the higher frequencies. Even more telling is the consistent intensity across the frequency band. What is most puzzling is the regular periodicity. Commented Aug 13, 2020 at 0:38