The extension in a string, obeying Hook's law, is x. The speed of sound in

Question

The extension in a string, obeying Hook'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 :

Options:

A . 1.22 v

B . 0.61 v

C . 1.50 v

D . 0.75 v

Answer: Option A
:
A
From Hooke's law
Tension in a string (

T

)

\propto

extension (

x

)
and speed of sound in string

v

\propto

\sqrt{T}

Therefore,

v \propto \sqrt{x}

X

is increased to 1.5 times i.e., speed will increase by

\sqrt{1.5}

times or 1.22 times. Therefore, speed of Sound in new position will be 1.22 v.

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