How can I play a single tone or custom wave with Delphi?

Question

I looked up some code, seems like everything is creating some math function waves, but I want to a single tone, or a custom wave made with custom single tones.

I read this How can I generate continuous tones of varying frequencies?

Which is close to my answer. Assumin I'm gonna use waveOutWrite like in the above link, I can't seem to figure out how the amp/freq is calculated for each Sample in HWAVEOUT.

In the code from the link It's done like this: Samples[i] := round(vol*sin(omega*t));

Assuming I want a 15kHz freq single tone with some amp (does not matter which), how would a Sample[1] be calculated?

Answer 1

A continuous (in time) sine wave can be defined as A*sin(2*PI*f*t), where A is some amplitude, PI is, well, 3.14..., f is the tone frequency in Hertz and t is time in seconds.

Now, since you don't have continuous time, since your time is discrete, you substitute dt*i in place of t and get A*sin(2*PI*f*dt*i), where dt is the time between samples or 1/sample rate and i is the sample number. You can spell it out as A*sin(2*PI*(f/Fs)*i). Beware that once you choose a certain sample rate Fs (in samples/second or simply Hz), the highest tone can never be greater than Fs/2 Hz.