Question about the calculation of adding certain SNR background noise to audio in tutorial

The tutorial address is as followed:
The part confuses me most is in this picture:

My question is: how does this code work? what’s the principle of mathmatics and derivative process behind it?
Any reference is appreciated.

According to Wikipedia

{athrm {SNR_{{dB}}}}=10og {{10}}eft({rac {P{{athrm {signal}}}}{P_{{athrm {noise}}}}}ight).

Given a desired SNR value, you just need to scale your speech signal so that the output of the above formula is equal to the desired one.

Thanks, I understand now. But why divided by 2 at last?

It’s just a practical operation to avoid value overflow. If the dtype of the waveform is float, the value range must be [-1, 1]. I would recommend dividing the noisy speech signal by the max absolute value, which can guarantee such range.