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The extension in a string obeying Hooke'...

The extension in a string obeying Hooke's law is x. The speed of sound in the stretched string is `v`. If the extension in the string is increased to `1.5 x`, the speed of sound will be

A

1.22 v

B

0.61 v

C

1.50 v

D

0.75 v

Text Solution

Verified by Experts

The correct Answer is:
A
Speed of sound in a stretched string us `v= sqrt(T/mu)" "... (i)`
where I is the tension in the string and u is mass per unit length.
According to Hooke.s law, `F prop x :. T prop x" "...(ii)`
From (i) and (ii), `vpropsqrtx,v.propsqrt(1.5)x`
`:. v. = sqrt(1.5)v=1.22v`
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