Is there a way to model sound wave interference patterns using Phased Array System Toolbox?

I am trying to find a way to model the constructive/destructive interference patterns for sound speakers in a room, i.e. concentrating sound in a specific part of the room through creating constructive interference from several non-directional (aka regular) speakers. I have been looking at the Phased Array System Toolbox (because I am thinking about an array of speakers) and think that might be the best fit for what I am looking for. Not sure if there is another Toolbox out there that does similar things or the Phased Array System is the best fit for this? Thank you!

[Umar]

Hi Janet,

In my opinion, Phased Array System Toolbox is indeed a robust choice for designing and simulating speaker arrays. It allows you to control the phase and amplitude of individual speakers to create desired interference effects. Another toolbox that can be useful for this purpose is the Audio Toolbox, which provides functions for audio processing and manipulation. For more information regarding this toolbox, please refer to

https://www.mathworks.com/products/audio.html

However, for precise control over interference patterns and beamforming, the Phased Array System Toolbox is often the preferred choice. Let me illustrate this with a simple example:

% Example code for creating a phased array of speakers
numSpeakers = 4;
array = phased.ULA('NumElements', numSpeakers, 'ElementSpacing', 0.5);
collector = phased.WidebandCollector('SensorArray', array, 'PropagationSpeed', 343);

So, by utilizing the capabilities of the Phased Array System Toolbox, you can efficiently model and simulate sound interference patterns to achieve your desired acoustic effects in a room. Good luck!

[Janet Sit]

Ah thank you Umar!!! Knowing I am on the right track is super helpful!

[Umar]

Hi Janet,

Thank you for your kind words and positive feedback. I am glad to hear that you found the information helpful and that you feel confident in the progress you are making. Please do not hesitate to reach out if you have any further questions or need additional assistance.

Answer 1

[Muskan]

Hi,

As per my understanding to model constructive and destructive interference patterns for sound speakers in a room, the Phased Array System Toolbox in MATLAB is indeed a very suitable tool.

You can follow the following steps in order to acheieve the same:

1. Define the Speaker Array: Set up an array of speakers with specific positions and properties.
2. Model the Sound Propagation: Simulate the propagation of sound waves from the speakers.
3. Analyze Interference Patterns: Calculate and visualize the interference patterns in the room. You can visualize the results by using the pattern function in MATLAB.

Here is a sample code on how you can do the same:

% Define parameters
f = 1000; % Frequency of the sound wave (Hz)
c = 343; % Speed of sound (m/s)
lambda = c / f; % Wavelength
d = lambda / 2; % Distance between speakers
numSpeakers = 10; % Number of speakers in the array

% Create speaker array
speakerArray = phased.ULA('NumElements', numSpeakers, 'ElementSpacing', d);
fc = f; % Carrier frequency

% Define the signal
t = 0:1/44100:1; % Time vector
signal = sin(2 * pi * f * t)'; % Sine wave signal

% Define the direction of the sound (azimuth, elevation)
% Note: Azimuth and elevation should be in degrees
azimuth = 0; % Angle in the x-y plane
elevation = 0; % Angle from the x-y plane up to the z-axis

% Collect and visualize array response
collector = phased.WidebandCollector('Sensor', speakerArray, 'SampleRate', 44100, 'PropagationSpeed', c);
receivedSignal = collector(signal, [azimuth; elevation]); % Direction [azimuth; elevation]

% Plot array response
pattern(speakerArray, fc, 'PropagationSpeed', c);
title('Array Response');

You can also refer to the following documentation on Array Geometries and Analysis to get a better understanding of array responses: https://www.mathworks.com/help/phased/array-geometries-and-analysis.html?s_tid=CRUX_topnav

I hope this helps!

[Janet Sit]

Thank you Muskan! This is super helpful as well and gives me lots of think about/work with (as a relatively new person to MatLab). Thank you!!!!!

[Umar]

Hi Muskan,

I do appreciate your support and sharing your knowledge.