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Transverse Wave Interference

by crazy_craig
Tags: interference, transverse, wave
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crazy_craig
#1
Sep11-10, 01:56 PM
P: 9
1. The problem statement, all variables and given/known data

What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.3 times that of the common amplitude of the two combining waves? Express your answer in (a) degrees, (b) radians, and (c) as a fraction of the wavelength.

2. Relevant equations

Same frequency and amplitudes results in:

y(x,t)=2ymcos(1/2Φ)sin(kx +/- wt +.5Φ)


3. The attempt at a solution

Amplitude of resultant wave = 2ymcos(1/2Φ)

2ymcos(1/2Φ)=2.3ym

solving for Φ :

2arccos(1.3/2)=Φ which is 1.7rad

However, I'm not sure how to express this in terms of the wavelength.
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lewando
#2
Sep11-10, 09:33 PM
PF Gold
P: 1,053
Just looking for fraction of the wavelength. A whole wavelength would be 2*pi rad worth of phase, yes?
crazy_craig
#3
Sep12-10, 12:29 AM
P: 9
That's what I had thought. Actually, I had done: 1.7/2pi, but I didn't put parenthesis around 2pi on my calculator. Jeez. Well, I guess the semester just started. Thank you lewando!


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