This is fantastic.  I appreciate your efforts to add a user interface, and think your code is quite excellent - you clearly understood the way the function works and kept its essential qualities together.

It would take some experimentation here to optimize this app.  I have, in my original implementation, 5 free parameters which yield the waveform, plus one extra (r) for the sample rate.  In retrospect my code is sloppy because I'm certain the most important parameter for the sound effect is the constant you called x, which is the frequency numerator of Sin[ x / (t + 1e-8].  You are correct to let this be directly manipulated and to correlate it with what I originally called f.

In general, for a simple user interface with fewer user inputs, keeping all the input constants as integer multiples of one another is a good fail safe guess.