You really can't handle the 22 kHz sinusoidal frequency at 44.1KB / s, and you can't increase the maximum sample rate above this, I suppose. Perhaps you can use 48 kHz, I vaguely remember that this is a supported rate.
On the other hand, you absolutely can make a square wave with a frequency of 22.05 kHz with a frequency of 44.1 fps, which will have several insanely high harmonic frequencies. Maybe the dog whistle app is working?
If absolute frequency control is not critical, you will get better results by rounding your frequencies to a multiple of the sampling frequency. That way, you can at least ensure that anti-aliasing doesn't give you low-frequency hits.
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