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Two vibrating springs 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, one of the lengths L with frequency f1 and the other with frequency f2. The ration is given by?

(a) 2

(b) 4

(c) 8

(d) 1

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Correct option is (d) 1

For explanation: f=1/2l×√(T/m)=1/2l×√(T/(πR^2 ρ))=1/2lR×√(T/πρ)

As T and ρ are the same for both strings,

f∝1/lR

For the first string,

f1∝1/L2r

For the second string

f2∝1/2Lr

Hence

f1/f2 =1.

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