Adiabatic Propagation of Sound Waves

Another example of adiabatic change in the atmosphere is found in the propagation of sound waves. Sound waves are longitudinal waves which travel by compression and rarefaction of air parcels. Newton was the first to compute the velocity of sound in air by using the relation where E is isothermal volume elasticity which in the case of an ideal gas is equal to pressure, p.

However, the velocity of sound computed by (3.4.15) differed from observed values. The cause for the discrepancy was found by Laplace who pointed out that the process of movement of sound waves in the air by compression and rarefaction was not isothermal but adiabatic. The changes in pressure and temperature took place so rapidly that there was little time for heat to leave the system. Now, it is readily shown (see Appendix-2) that when the process is adiabatic, the adiabatic modulus of elasticity is y times that of isothermal modulus of elasticity. The corrected velocity of sound is, therefore, given by the expression (3.4.16):

A mean value of sound velocity in the atmosphere is about 330m s

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    Why is the process of sound wave propagation is adiabatic?
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