Speccy Spectrum Analyzer APP
It has a wide range of uses, such as: assessing environmental noise, tuning speaker systems, identifying audio signals obscured to the human ear by noise or simply testing the microphone on your device. You could use Speccy to compare the quality of different types of headphones, test signal generators or measure audio signals just outside human perception. It apparently has also been used successfully to find gas leaks.
Speccy provides the most 'analysis window functions' (the 13 most popular for audio engineers) and, for your added peace of mind, the only permission Speccy needs is microphone access.