By obtaining the equation of speed of sound wave, obtain equations of sound wave in different medium.

Explanation

In longitudinal wave the consituents of the medium oscillate forward and b ackward in the direction of propagation of the wave.
The property that determines the extent to which the volume of an element of a medium changes when the pressure on it changes is the bulk modulus B its dimensional formula is `M ^(1) L ^(-2).`
The longitudinal waves in a medium travel in the form of compressions and refrefactions or changes in the density `rho.` The dimension of density is `[Ml ^(-3)].`
Thus, the dimension of the ratio `(B)/(rho)` is,
`therefore ([B])/([rho ]) = ([ M ^(1) L^(-2) T ^(-2)])/([M^(1) T ^(-3) T ^(0)]) = [L^(2) T ^(-2)]`
`therefore ([B])/([rho ])prop v ^(2)`
Therefore on the basis of dimensional analysis the most appropriate expression for the speed of `v = C sqrt ((B)/(rho))`
What C is a dimensionaless constant and can be shown to be unity.
Thus, the speed of longitudinal waves in a medium is given by,
`v = sqrt ((B)/(rho ))`
The speed of propagation, of a longitudinal wave in fluid therefore depends only on the bulk modulus and the density of the medium.
For the case like solid bar or rod, the relevant modulus of elasticity is the Young.s modulus.
Hence, Young.s modulus should be taken in place of bulk modulus for such case.
The speed of a longitudinal wave in the bar is given by,
`v= sqrt ((Y)/(rho))` where, Y = Young.s modulus