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Question

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5×102 kg and its linear density is 4.0×102 kg m1. The tension in the string is approximately -

A
300.47N
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B
425.25 N
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C
247.27 N
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D
500 N
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Solution

The correct option is C 247.27 N
Mass of wire (m)=3.5×102 kg
Linear density (μ)=4×102 kg/m
μ=mL
L=mμ=3.5×1024×102=78m

In fundamental mode , L=λ2
λ=2L=74m
Now velocity of transverse wave is,
v=fλ=45×74=78.75m/s
Using v=Tμ
T=μv2
T=4×102×(78.75)2=248 N

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