According to the transform $$w(u,s)=\frac{1}{\sqrt{s}}\int _{-\infty }^{\infty }x(t) \psi ^*\left(\frac{t-u}{s}\right)dt,$$ the frequency should be $f=\omega/(2\pi)=1/(2\pi s)$ (is it right?), where the discretized s' are calculated from octaves and voices, following $$s_{\text{oct},\text{voc}}=\alpha 2^{\text{oct}-1} 2^{\text{voc}/\text{nvoc}}$$ But from one second of 20Hz's humming:
WaveletScalogram[ContinuousWaveletTransform[
Table[Sin[40 Pi x] , {x, 0, 1, 1/2048}],
GaborWavelet[], {6, 4}, WaveletScale -> 10]]
one can see that coefficients mainly lie in the 4th octave (in this case $\alpha=10$ and the corresponding scale {4,4}=160), which is contrast to $f=1/(2\pi s)$. I must have got some silly errors. So what is the correct frequency formula? Thank you!