Question

The speed of sound in dry air at NTP is 332 metres `//`sec. Assuming air as composed of 4 parts of nitrogen and one part of oxygen, calculate velocity of sound in ocygen under similar condistions, when the densities of oxygen and nitrogen at NTP are in the ration of `16:14` respectively .

Answer 1

Here, velocity of sound in air,
`v_(a)=332metres//sec. `
We have to calculate velocity of sound in oxygen, i.e., `v_(0)=?`
Also, `(rho_(0))/(rho_(n))=(16)/(14)`
Let volume of oxygen in air `=V`
`:.` Volume of nitro gen in air `=4V`
Total volume of air` =V+4V=5V`
Mass of oxygen in air `=Vxx16=16V`
Mass of nitrogen in air `4Vxx14=56V`
Total mass of air `=16V+56V=72V`
`:.` density of air,
`rho_(a)=(t otal mass of air)/(t otal volume of air)=(72V)/(5V)=14.4`
As, `(v_(0))/(v_(a))=sqrt((rho_(a))/(rho_(0)))`
`:.(v_(0))/(332)=sqrt((14.4)/(16))=sqrt(0.9)=0.9487`
`:. v_(0)=332xx0.9487=314.77ms^(-1)`