lecture29 - 8.0m 0.35m 3m Solution Intensity I Intensity I...

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Interference of Sound Interference of Sound Waves Waves
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Interference Interference 2 waves, of the same frequency; out of phase. Eg. y 1 = A 0 sin (kx - ϖ t) y 2 = A 0 sin (kx - t + φ ) Then y R =A R sin (kx- t+ /2) , and the resultant amplitude is A R =2A 0 cos(½ φ 29 . Identical waves which travel different distances will arrive out of phase and will interfere, so that the resultant amplitude varies with location.
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Example: Two sources, in phase ; waves arrive at P by paths of different lengths : At P: 1 0 1 2 0 2 sin( ) sin( ) y A kx t y A kx t ϖ = - = - detector S 1 S 2 P x 1 x 2
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Phase difference : Then (using trig), at detector: 1 2 1 2 ( ) ( ) ( ) kx t kx t k x x k x ϖ - - - = - = ∆ 2 radians k x x π ϕ λ = ∆ = ∆ 1 2 0 (2 cos )sin( ( ) ) 2 2 2 R x x y A k t + = - + Define x to be the path difference =
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Example Example A pair of speakers is separated by 3.0m and driven by the same oscillator. The listener walks perpendicular from a point on the centerline 8m away to a distance of 0.35m before reaching the first minimum in sound intenstiy. What is the frequency of the oscillator?
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Unformatted text preview: 8.0m 0.35m 3m Solution Intensity I Intensity I I = Power per unit area Units: W / m 2 (the area is measured perpendicular to the wave velocity) Intensity is proportional to (resultant amplitude) 2 Two sources, each with amplitude A o , intensity I o , phase difference o tant amplitude 2 cos( ) 2 R resul A A = 2 2 o max 4 cos ( ) cos ( ) 2 2 R I I I = = Notes : 1) Maximum I R is 4 x I O 1) Maxima when = 0, 2, 4, 6 , 1) Minima (zero intensity) when = , 3, 5 , 1 x = /2, 3 /2 , 5 /2, 11 x = 0, , 2 , Note: The sources are in phase !!! 2 speakers, same intensity, in phase; f = 170 Hz (so = 2.0 m when speed of sound is 340 m/s) At the position x=9 m, find the intensity in terms of the intensity of a single speaker 6 m x detector Example Solution...
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This note was uploaded on 01/13/2011 for the course PHYSICS Physics 1E taught by Professor Venus during the Winter '03 term at McMaster University.

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lecture29 - 8.0m 0.35m 3m Solution Intensity I Intensity I...

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