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# lecture30 - Interference of Sound Waves Waves Interference...

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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.
Quiz y You are located at position y, whereyou can hear a loud sound - the first maximum in intensity from two speakers. Thespeakers are then connected ‘out of phase’ (difference of π ). What will you hear? A) no change– sameloud sound B) no sound C) something between ‘no sound’ and ‘loud sound’

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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
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 + = - +

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