Sound around you is analyzed with a Fast-Fourier Transform, or "FFT" (this app's namesake). The FFT is computed with over 212 samples, giving roughly 5 Hz resolution, allowing you to pinpoint exactly what frequencies are around you.

The spectrum of your audio is recalculated over 60 times per second to give you the the most responsive display. All graphics are rendered with OpenGL. There's no faster way to do it on the iPhone.

Single-tap to see the peak frequency.
Double-tap to pause.
Tap and hold to bring up a cursor, to analyze individual points.
It's that easy.

Spectral analyzers that perform this type of analysis can cost thousands of dollars, and you definitely can't fit them in your pocket. With Fourier, you'll always be able to pinpoint what frequencies are around you.