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Speed of sound in dry air at STP is 332 ...

Speed of sound in dry air at STP is 332 m/s. Assume that volume of air has nitrogen in 4 parts and oxygen in 1 part. If ratio of density of `N_(2)` to that of O, is 14:16, then find speed of sound in oxygen.

Text Solution

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Density of air ` =("total mass of air")/("total volume of air")`
`therefore rho _(a) = ("mass of " O_(2) + "mass of " N _(2))/("volume of " O_(2) + "volume of " N_(2))`
`= ((V rho _(O)) + (4 V xx rho _(N )))/( (V ) + (4 V ))= (rho _(O) + 4 rho _(N))/( 5) = (rho _(O) (1 + (4 rho _(N))/( rho _(O))))/(5)`
`= (rho _(O) {1 + (4 xx (14)/(16)) })/( 5) = 0.9 rho _(O)`
Now, speed of sound, `v prop (1)/(sqrt rho ) ( because v = sqrt (( gamma P )/( rho )))`
`therefore (v _(O))/( v _(a)) = sqrt (( rho _(a))/( rho _(O)))`
`therefore (v _(O))/( 332) = sqrt (( 0.9 rho _(O))/( rho _(O)))`
`therefore v _(O) = 314 .77 m//s`
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