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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 4The equation of stationary wave in string is, y=4sin(πx15)cos(96πt) Comparing above equation with y=2Asinkxcosωt We get, k=π15 cm−1 ⇒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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