ch16-p053 - 53(a The waves have the same amplitude the same...

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y 1 = y m sin( kx ω t ), y 2 = y m sin( kx + t ). The amplitude y m is half the maximum displacement of the standing wave, or 5.0 × 10 –3 m. (b) Since the standing wave has three loops, the string is three half-wavelengths long: L = 3 λ /2, or λ = 2 L /3. With L = 3.0m, λ = 2.0 m. The angular wave number is k = 2 π / λ = 2 π /(2.0 m) = 3.1 m –1 . (c) If v is the wave speed, then the frequency is () () 3 100m s 3 50 Hz. 22 3 . 0 m vv f L == = = λ The angular frequency is the same as that of the standing wave, or ω = 2 π f π (50 Hz) = 314 rad/s. (d) The two waves are () ( ) ( ) 31 1 1 5.0 10 m sin 3.14m 314s y xt −− ªº ¬¼ and () (
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This note was uploaded on 04/16/2011 for the course PHYSICS 191262 taught by Professor Najafzadeh during the Spring '09 term at The Petroleum Institute.

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