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Question

Vibration in a string of length 60 cm fixed at both ends is represented by the equation, y=4sin(πx15)cos(96πt), where x and y are in cm and t in s. The number of loops formed in vibrating string will be

A
4
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B
3
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C
6
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D
5
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Solution

The correct option is A 4
The equation of stationary wave in string is,
y=4sin(πx15)cos(96πt)
Comparing above equation with
y=2Asinkxcosωt
We get,
k=π15 cm1
λ=2πk
λ=30 cm
For one loop of stationary wave, l=λ2=15 cm
Since string is fixed at both ends, they will act as nodes. Let (n) loops of stationary wave will be formed between both nodes.
L=nl
where L length of the string.
n=Ll
n=6015=4

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