# lecture32 - Beats Interference Text sections 18.7 18.1...

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Text sections 18.7; 18.1 Text sections 18.7; 18.1 Beats; Interference Practice: Chapter 18, problems 9, 51, 67 Beats Beats Two waves of different frequencies arriving together produce a fluctuation in power or amplitude. Since the frequencies are different, the two vibrations drift in and out of phase with each other, causing the total amplitude to vary with time. y time 1 beat

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time t in phase 180 o out of phase in phase Same amplitudes, different frequencies: ) cos( 1 0 1 t A y ω = ) cos( 2 0 2 t A y = Trigonometry: cos a + cos b = 2 cos [(a-b)/2] cos [(a+b)/2] Result: + = + = t t A y y y 2 cos 2 cos 2 2 1 2 1 0 2 1 slowly-varying amplitude SHM at average frequency The math:
Note maximum power when “amplitude” part is 2A 2 beats per cycle of t 2 cos 2 1 ω # beats/second = × 2 2 2 1 f f The beat frequency (number of beats per second) is equal to the difference between the frequencies:

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## This note was uploaded on 12/03/2009 for the course CHEMISTRY 1E03 taught by Professor Britz during the Spring '09 term at McMaster University.

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lecture32 - Beats Interference Text sections 18.7 18.1...

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