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

Options

A. 1.22v
B. 0.61v
C. 1.50v
D. 0.75v

Answer

A

Explanation

(a) According to the question , `T prop x, T' prop (1.5 x)`
We have, `v_(s) prop sqrt(T)" "(therefore v_(s)=sqrt((T)/(mu)))`
`therefore (v'_(s))/(v_(s))=sqrt((T')/(T))=sqrt((1.5x)/(x))=sqrt(1.5)`
The speed of sound `v'_(s)=sqrt(1.5)v_(s)=sqrt(1.5)v=1.22v`