Last modified on 7 August 2006, at 17:59

Waves/Beats

Waves : 1 Dimensional Waves
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Examples - Problems - Solutions - Terminology

BeatsEdit

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 ( \omega_1 t) + \sin ( \omega_2 t) = 2 \sin ( \omega_0 t) \cos ( \Delta \omega t) , (2.19)

where we now have \omega_0 = ( \omega_1 + \omega_2 )/2 and \Delta \omega = ( \omega_2 - \omega_1 )/2. What you actually hear is a tone with angular frequency \omega_0 which fades in and out with period T_{beat} = \pi / \Delta \omega = 2 \pi / ( \omega_2 - \omega_1 ) = 1 / ( f_2 - f_1 ) . (2.20)

The beat frequency is simply  f_{beat} = 1/T_{beat} = f_2 - f_1 . (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.


Waves : 1 Dimensional Waves
1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13
Examples - Problems - Solutions - Terminology