Waves/Beats
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Examples - Problems - Solutions - Terminology
[edit] Beats
Suppose two sound waves of different frequency impinge on your ear at the same time. The displacement perceived by your ear is the superposition of these two waves, with time dependence A(t) = sin(ω1t) + sin(ω2t) = 2sin(ω0t)cos(Δωt), (2.19)
where we now have ω0 = (ω1 + ω2) / 2 and Δω = (ω2 − ω1) / 2. What you actually hear is a tone with angular frequency ω0 which fades in and out with period Tbeat = π / Δω = 2π / (ω2 − ω1) = 1 / (f2 − f1). (2.20)
The beat frequency is simply fbeat = 1 / Tbeat = f2 − f1. (2.21)
Note how beats are the time analog of wave packets -- the mathematics are the same except that frequency replaces wavenumber and time replaces space.
