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  • Use the formula v= sqrt gamma P/rho to explain why the speed of sound in air (a) is independent of pressure.

Q.15.4 (a) Use the formula v=\sqrt{\frac{\gamma P}{\rho }} to explain why the speed of sound in air

(a) is independent of pressure,
                

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v=\sqrt{\frac{\gamma P}{\rho }}

Where \gamma \ and \ \rho are the Bulk's modulus and the density respectively

As we know

\rho =\frac{M}{V}

where M is molecular weight of air and V is the volume of 1 mole of air

\\v=\sqrt{\frac{\gamma P}{\rho }}\\ v=\sqrt{\frac{\gamma PV}{M}}

From the ideal gas equation PV=nRT

since we are talking about 1 mole we take n = 1

PV=RT

The expression for the speed of sound becomes

v=\sqrt{\frac{\gamma RT}{M}}

\gamma, M and R are constant therefore at constant Temperature the speed of sound in the air do not change and it is clear that speed is independent of velocity.

Posted by

Sayak

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