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Question

A wave given by equation y=8sin2π(0.1x2t) where x and y are in centimeters and t is in seconds. At any instant , the phase difference between two particles, separated by 2.0 cm along the x-direction, is,

A
18
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B
36
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C
54
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D
72
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Solution

The correct option is D 72
Given:
y=8 sin2π(x102t)
Δx=2 cm

writing the equation again we have,
y=8sin(2π10x4πt)
k=2π10=2πλ
gives, λ=10 cm

Now, the phase difference between the points is given by,
Δϕ=2πλ×Δx

Δϕ=2π10×2=2π5 rad

Δϕ=25×180=72

Hence, (D) is the correct answer.

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