The speed of sound in oxygen `(O_2)` at a certain temperature is `460ms^-1`. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)

Options

A. 460m/s
B. 500m/s
C. 650m/s
D. 1420m/s

Answer

D

Explanation

The speed of sound is given by
`v= sqrt(gamma R T)/( M )` , `v_(o_(2))= sqrt(((7)/(5)RT)/(32)) and v_(He)= sqrt(((5)/(3)RT)/(4))`
`(v_(o_(2)))/(v_(HO))= sqrt((7 xx 3xx 4)/(5 xx 32 xx 5)) rArr v_(Ho) = 460 xx 10 xx sqrt((2)/(21)) = 1420 m//s`
No option matches with the answer.