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Question

The displacement of a particle of a string carrying a travelling wave is given by y=3sin[6.28(0.50x50t)]
(xin cm, y cm, tin second).
What would be the speed of the wave?

A
200 cm s1
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B
150 cm s1
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C
100 cm s1
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D
50 cm s1
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Solution

The correct option is C 100 cm s1
Displacement of a particle on string(carrying a travelling wave) is given,
y=3sin[6.28(0.5x50t)]
where x, y are in cm, t is in seconds.
Comparing with equation of progressive wave,
y=Asin(kxωt)
We get
k=6.28×0.5 ; ω=6.28×50
We know that k=2πλ
2×3.14λ=6.28×0.5
λ=2 cm
and ω=2πf
2πf=6.28×50
6.28f=6.28×50
f=50 Hz
Speed of wave is,
v=fλ
v=50×2=100 cm s1

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