The speed of sound in air at temperature T and pressure p is v. When the temperature is increased to 2T and the pressure is reduced to `p /2,` then the speed is changed to

Options

A. 2v
B. v
C. `sqrt2 v`
D. `(v)/(sqrt2)`

Answer

C

Explanation

Speed of sound in air does not depend on pressuure, but direactly proporational to the root of temperature, i.e.
`v propsqrtT implies (v_(2))/(v_(1)) = sqrt((T_(2))/(T_(1)))`
Given ,`T_(1)= T and T_(2)=2T.`
`v _(1)=v,v _(2) =?`
`(v_(2))/(v ) = sqrt((2T)/(T))impliesv_(2)=sqrt2v`