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I am recording in a very large room and getting sound reflections off the walls. So I was going to buy acoustic foam for the walls. Before I buy the foam, I wanted to measure the frequency response of the walls because there are different foams that target different frequency ranges. I have set up an audio system in the room to measure the reflections.

What type of waveform should I play to measure the reflections? I was considering the following:

  1. An impulse. This seems like the obvious choice, however I can't get a very loud impulse noise from my speaker. I am using waveform where the audio level jumps from its lowest point to its highest point and back over a single point.
  2. A fast sine sweep. I could use a sine sweep that plays very quickly. It would have to play quick enough that it finishes before the reflections return back.
  3. Pink noise. Because there is randomness in pink noise, I would probably have to do multiple tests and average the results.
  4. Single frequency sine waves. I could go through the frequency spectrum at 1/3 octaves and make a recording for each frequency. This would be more time consuming.
  • Use sweep sine. And no, you don’t have to play it quickly. In fact the longer the sweep you get better impulse to noise ratio. – jojek Aug 11 '20 at 20:16
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If it helps, there are a couple of tools you can use to measure room acoustics. REW https://www.roomeqwizard.com/ and Sonarworks reference https://www.sonarworks.com/reference.

It's been quite a while since I used either of these tools however I do remember sonarworks' calibration test being the most thorough. The wizard makes things very simple also. It essentially covers everything on your list in a single test and takes measurements from different listening positions. Probably the most important thing you'll need is a calibrated microphone.

There's also a handy visualizer from gik acoustics that allows you to model your listening environment in 3d space to help determine where to place panels. https://www.gikacoustics.com/room-acoustics-visualizer/

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Well, the problem you are trying to tackle is not one that has a clear solution. There are various research groups as well as companies' R&D departments that are trying to provide their solutions to your problem.

The issue here is the "multidimensionality" of the problem at hand. You have time (one dimension), frequency (second dimension, related to the first one though) and direction (three dimensions) to care about.

The simplest approach to the problem would be to take various Impulse Response (IR) measurements at various places in the room you are measuring and from that, or maybe even better, the Energy Time Curve (ETC) isolate the reflections, perform some kind of frequency analysis (FFT or filterbanks are two of the most well known) and see what is the difference between the direct and the reflected sound, thus concluding about the frequency-dependent absorption of the wall causing the reflection.

Well known alternatives are the Spatial Decomposition Method (SDM) and various Beamforming and Direction of Arrival (DoA) estimation techniques (MUSIC could be a good candidate since it can provide frequency "super-resolution").

IR and SDM methods use impulse response measurements, for which sine sweeps are "ideal", but other signals such as Pseudorandom Noise, or MLS can be used (please refer to Time Delay Spectrometry - TDS - and other measurement techniqes such as Maximum Length Sequence - MLS - for more information).

Beamforming and DoA estimation techniques can possibly use arbitrary signals but are more difficult to implement, they need at least two microphones/sensors (knowledge of the setup is a prerequisite) and the need for specialised software or custom implementation is needed.

All in all, the simplest possible case would be to use some measurement software (such as SMAART, ARTA or REW) with one omnidirectional microphone to get impulse responses and isolate individual reflections.

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You need a gated pulse so microphone records only the reflection. A single pulse can provide a frequency response curve with the proper software

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