# Insensitivity of the human ear to phase.

The human ear is insensitive to phase in the Fourier expansion of a periodic waveform: given a periodic signal $A_0/2+\sum\limits_{n=0}^{+\infty}A_n\cos(nt+\phi_n)$, we can replace it with $A_0/2+\sum\limits_{n=0}^{+\infty}A_n\cos(nt+\tilde\phi_n)$, where we changed the phase angles $\phi_n$ with randomly chosen $\tilde\phi_n$. The two waveforms are possibly very different, but sound exactly the same!

Material Type
Worksheet
Tags
fourier  series  phase  angle  human  ear
Target Group (Age)
19+
Language
English (United States)

GeoGebra version
4.4
Views
1257

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