Generating sound of particular frequency matlab

Question

I want to generate a high frequency (single) tone. I am using matlab (any other platform/tool for the same will also work). I am using the following snippet which I wrote by referring to various sources achieving similar specification.

amp = 10;
Fs = 44100;
duration = 60;
freq = 20000;
t = (0:1/Fs:duration-1/Fs);
%t = linspace(0,duration,Fs*duration);

wave = amp*sin(2*pi*freq*t);
%sound(wave, Fs);

audiowrite('20KHz-pilot.wav',wave,Fs);

draw_spec = 0;
if(draw_spec == 1)
    NFFT = 2048;
    wave = wave(1:NFFT);
    y = fft(wave);
    y = abs(y/NFFT);
    y = y(1:NFFT/2+1);

    % as 0 and Fs don't have any alias while others do
    % we need to double the power of the other frequencies since we are
    % converting from 2 sided power spectrum to single sided spectrum.
    y(2:end-1) = 2*y(2:end-1);

    f = Fs*(0:(NFFT/2))/NFFT;
    plot(f,y);
end

The problem I am facing is that when I load the file in audacity it shows frequencies other than 20KHz in fact 20Khz is not there in spectrogram. Further when I play the sound I can hear it which should not be the case (most adults have audio hearing range upto 18Khz). Also plotting spectrum of the wave in matlab only shows 20KHz.

I have tried to use common conventional variable names so the code should be pretty self explanatory.

I am not able to find where I am making a mistake, is there a mistake in the code or is it that due to sampling rate etc. there are other frequencies also generated (aliasing or similar concepts). I tried playing the sound on different speaker systems to check if it could be a hardware issue but that was not the case.

NOTE: I have browsed through multiple resources with similar question title as mine, unfortunately none of them were able to help me. Thus, I resorted to posting this question.

Answer 1

Try wave = amp*sin(2*pi*freq/Fs*t) instead. Since Fs maps to $2 \cdot \pi$, freq maps to $\frac{2\cdot\pi\cdot {\tt freq}}{\tt Fs}$.

Could be useful for reference on Wikipedia.

Answer 2

I initially thought oxuf's and Marcus Müller's answers were right and I was not normalizing the frequency but that was not the case since my time vector takes values t = 0:1/Fs:duration, thus my time vector is in seconds (it does not take integer values for samples but represents the clock time at the ith sample), due to which my frequency should be in hertz and not normalized.

I played the audio after implementing oxuf's method which led to an audio with very low frequency which was inaudible to human ear so I thought problem solved and it must be of high frequency but that was not the case, the issue was something else.

@MBaz's comment led me to the answer, I had given a value of 10 to amplitude while its range should be from -1 to 1 from the MATLAB documentation of audio write and so MATALB was truncating the values which were higher than 1 in magnitude to 1 itself which was causing the issue, changing the value of amp to 1 solved the problem.

Below shows the waveforms in Audacity: The lower waveform for amp = 10 is truncated and thus there are other frequencies in the signal.

For reference these are the spectrograms for the 2 audio: https://i.sstatic.net/8MeTx.png (could not embed third image due to lack of reputation on this forum)