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Question

A wave moves with speed 400 m/s on a wire , which is under a tension of 900 N. If the wave moves with 450 m/s, then the change in tension of the wire is

A

250 N
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B
+250 N
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C
+239 N
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D
239 N
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Solution

The correct option is C +239 N
Speed of a transverse wave on wire is
v=Tμ ......(1)
Differentiating with respect to time on both sides,
dvdt=12μTdTdt .........(2)
From (1) and (2) we have

dvv=12dTT

dT=2T×dvv
From the data given in the question ,
dT=2×900×(450400)400=+225 N
Tension should be increased by 225 N
Thus, option (c) is the correct answer.

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