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Question

Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n1 and the other with frequency n2. The ratio n1/n2 is given by.

A
2
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B
4
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C
8
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D
1
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Solution

The correct option is D 1
Fundamental frequency n=12lTπ2ρ
where m= Mass per unit length of wire

n=1lr
n1n2=r2r1×l2l1=r2r×2LL=11

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