Velocity of sound in `O_(2)` gas is 460 `ms^(-1)` at certain temperature. Velocity of sound in He gas at the same temperature would be .......
(Consider both the gases to be ideal).

Options

A. `1419 ms ^(-1)`
B. `460 ms ^(-1)`
C. `500 ms^(-1)`
D. `650 ms ^(-1)`

Answer

A

Explanation

We have, `v = sqrt ((gamma RT)/( M _(0)))`
considering oxygen and helium gases as first and second gas respectively,
`(v_(1))/(v _(2) ) = sqrt ((T _(1))/( T _(2)) xx ( M _(02))/( M _(01)) xx (gamma _(1))/( gamma _(2))) " "(because ` R is constant)
`therefore (460)/(v _(2)) = sqrt(1 + (4)/( 32) xx (7//5)/(5//3))" "(because T_(1) - T _(2))`
`therefore v _(2) = 460 xx sqrt ((32)/(4) xx (5)/(3) xx (5)/(7)) = 1419 (m)/(s)`