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The velocity of the wave in of sound depends on bulk modulus and density of the medium derive the formula of velocity

Asked by umeshlochab887 | 12 May, 2021, 06:17: PM
Velocity of sound v in a gaseous medium is related to Bulk modulus B  and density ρ .

Velocity of sound v is given as

.................................(1)
Bulk modulus B is given as

..............................(2)
When sund waves is propagated in a gaseous medium, compression and rarefaction processes are fast ,
hence we can assume adiabatic condition for change in pressure and volume.

For adiabatic process, we have , where C is constant and γ is ratio of specific heat.

Hence we get
Hence from eqn.(2) , we get , ....................(3)
Density ..........................(4)
where n is number of moles in a volume V and M is molar mass of gas.

Using eqn.(3) and eqn.(4) , we rewrite eqn.(1) as

In above expression, we have used ideal gas equation , pV = ( n R T )

Answered by Thiyagarajan K | 12 May, 2021, 08:00: PM

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