why does the sound with different sampling frequency sounds the same ?

Dear people,

I am trying to write an audio with the following lines. However, every after I write an audio into a file and play it, they sound the same no matter what the sampling frequency is.

clear all
clc

FrequencySampling = 2500;                                     % 2500 for safe 10000 for shock
duration =17;
repeats=1;

t  = linspace(0, duration, FrequencySampling*duration+1);      % Time Vector + 1 sample
t(end) = [];                                                   % remove extra sample
w = 2*pi*1000;                                                 % Radian Value To Create 1kHz Tone                              
                                                              
for i=1:repeats
        s = sin(w*t);
        sound(s,FrequencySampling);
        pause(5)                                               %ITI 60 sec 
end
audiowrite('shock.wav',s,FrequencySampling);
    

Please recommend me any possible reasons or let me know if I have done sth wrong.

Answer 1

[Akira Agata]

That's the basic of the 'Sampling theorem'. As long as frequency component of the signal is less than Nyquist frequency ( = sampling frequency * 0.5), the original signal can be re-generated.

Looking at your code, the signal frequency is 1 [kHz] and both sampling frequencies (2.5 [kHz] and 10 [kHz]) satisfy the Nyquist condition. So the regeneratd signal sounds the same.

[Yanjika O]

Then, how to make them different in terms of sampling frequency (2.5kHz and 10kHz)?

[Akira Agata]

Then you need to compare one re-generated signal with sufficient sampling frequency (= satisfies Nyquist condition) and another signal with insufficient sampling frequency.

The following is an example. (please compare the two .wav files with different sampling frequency)

load handel.mat

% Sufficient sampling frequency (8192 [Hz])
audiowrite('handel_8192.wav',y,Fs);

% Insufficient sampling frequency (4096 [Hz])
audiowrite('handel_4096.wav',y(1:2:end),Fs/2);