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Question

A 4 m long rope, having a mass of 40 g is fixed at one end and is tied to a light string at the other end. Find the tension in the string if the difference between frequencies of consecutive overtones is 40 Hz.

A
1024 N
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B
512 N
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C
2048 N
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D
1000 N
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Solution

The correct option is A 1024 N
From formula for string fixed at one end,
fn=2n+14LTμ
and for (n+1)th overtone,
fn+1=2(n+1)+14LTμ=2n+34LTμ
From question,
fn+1fn=40 Hz
2n+34LTμ2n+14LTμ=40
14LTμ[2n+3(2n+1)]=40
12LTμ=40T=(40×2L)2×μ
From given data,
μ=40×1034=102 kg/m
L=4 m
T=(40×2×4)2×102=1024 N

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