The velocity of sound is `v_(s)` in air. If the density of air is increased to 4 times, then the new velocity of sound will be

Options

A. `(v_(s))/(2)`
B. `(v_(s))/(12)`
C. `12v_(s)|`
D. `(3)/(2)v_(s)^(2)`

Answer

A

Explanation

`vprop(1)/(sqrt(rho))implies(v_(1))/(v_(2))=sqrt((rho_(2))/(rho_(1)))=sqrt((4)/(1))=2`
`implies (v_(s))/(v_(2))=2impliesv_(2)=(v_(s))/(2)`. `[because v_(1)=v_(s)]`