sound generation using MATLAB

clc;
clear all;
close all;
fs=24000; %sampling frequency
f=100000; %frequency of the sound wave
t=0:1/fs:10;
y=sin(2*pi*f*t);
sound(y);

I generated a sound wave using the above code. Why is it audible? I set its frequency to more than 20kHz which is the limit of the human ear.

what's wrong here? Does it have to do with the speakers? or the code?

Answer 1

[Image Analyst]

It's called aliasing. Sampling at rate lower than the Nyquist frequency will give signals that look like they are oscillating at a lower frequency. See the Wikipedia article on it: Wikpedia on Aliasing

[kartik singh]

Thanks a lot. I understood what was wrong.

Answer 2

[Stephan]

Hi,

think about your sampling frequency. Can it really work to sample a signal of 100kHz with a sample rate of 24kHz? Or do you get some useless stuff?

Consider:

fs=2.4; %bad sampling frequency
fs2 = 240 % good sampling frequency

f=10; %frequency of the sound wave

t=0:1/fs:2;
t2 = 0:1/fs2:2; 

y=sin(2*pi*f.*t);
y2=sin(2*pi*f.*t2); 

plot(t,y,t2,y2)

which gives the following plot:

:

This does not look rigth for the blue line which corresponds to a much too low sample frequency. The higher sample rate gives a correct result.

https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

Best regards

Stephan

[kartik singh]

Thanks for the answer. My query got cleared.

[Stephan]

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