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Question
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of 0.5 m
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Solution
Given, wave functions are y = 2 cos 2π (10t – 0.0080x + 3.5)
= 2 cos(20πt – 0.016πx + 7π)
Now, the standard equation of a travelling wave can be written as y = a cos(ωt – kx + `phi`)
On comparing with the above equation, we get
a = 2 cm
ω = 20π rad/s
k = 0.016π
Path difference = 4 cm
Δ`phi = (2π)/λ xx (0.5 xx 100)` ......[∵ Path difference = 0.5 m]
= 0.016π × 0.5 × 100
= 0.8π rad
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