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# 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 thesamefrequency; out of phase. Eg. y 1 = A 0 sin (kx - ϖ t) y 2 = A 0 sin (kx - ϖ t + φ ) Then y R =A R sin (kx- ϖ t+ φ /2) , and theresultant amplitudeis A R =2A 0 cos(½ φ 29 . Identical waves which travel different distances will arrive out of phaseand will interfere, so that the resultant amplitude varies with location.
Example: Two sources, in phase ; waves arriveat 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 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 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 ϕ ϕ ϖ + = - + Define x to bethepath difference ϕ ϕ =
Example Example A pair of speakers is separated by 3.0m and driven by the same oscillator. Thelistener walks perpendicular from a point on thecenterline8m away to a distanceof 0.35m before reaching the first minimum in sound intenstiy. What is thefrequency 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 φ o tant amplitude 2 cos( ) 2 R resul A A ϕ = 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 φ = 0, 2π, 4π, 6π , … 1) Minima (zero intensity) when = π, 3π, 5π , … 1 x = ± λ /2, ± 3 λ /2 , ± 5 λ /2,… 11 x = 0, ± λ , ± 2 λ ,… Note: The sources are in phase !!! 2 speakers, same intensity, in phase; f = 170 Hz (so λ = 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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lecture29 - 8.0m 0.35m 3m Solution Intensity I Intensity I...

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