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
B. 460
C. 500
D. 650

Answer

A

Explanation

Speed of sound in a gas is,
`v = sqrt(( gamma RT)/( M _(0)) )implies v prop sqrt ((gamma )/( M _(0)))`
`(because` R and T are constants)
`therefore (v _(1))/( v _(2)) = sqrt (( gamma _(1))/( gamma _(2)) xx ( M _(02))/( M_(01)))`
Taking oxygen and helium gas as first and second gas,
`(460)/(v _(2)) = sqrt((7//5 )/( 5//3) xx (4)/(32))= sqrt (( 7)/(5) xx (3)/(5) xx (1)/(8))`
`therefore v _(2) = 460 xx sqrt ((200)/( 21)) = 1219.59 (m)/(s) ~~ 1419 m//s`