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The speed of sound in oxygen (O2) at a c...

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)

A

`500 ms^(-1)`

B

`650 ms^(-1)`

C

`330 ms^(-1)`

D

`1420 ms^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Speed of sound -
`v= sqrt((gammaP)/rho)=sqrt((gammaPV)/M)=sqrt((gammaRT)/M)`
`(v_(O_2))/(v_(He))=sqrt((gamma_(O_2))/(gamma_(He))xx(M_(He))/(M_(O_2)))=sqrt(7/5 xx3/5 xx4/32)`
`implies v_(He)=sqrt(8xx(25)/21)xx460 =1420 m//s`
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