Velocity of sound in any elastic medium
It is given by ![1864_Velocity of Longitudinal Wave.png](https://www.expertsmind.com/../CMSImages/1864_Velocity of Longitudinal Wave.png)
(i) In solids v = √(Υ/ρ) ; where Y ¾ Young's modulus of elasticity.
(ii) In a liquid and gaseous medium v = √(B/ρ) ; where B ¾ Bulk modulus of elasticity of liquid or gaseous medium.
(iii) As solids are most elastic while gases least EBksi > Enzo > EkSI i.e. . So the velocity of sound is maximum in solids and lowest in gases, hence vBksi > vnzo > vkSI
(iv) The speed of sound in case of extended solid (crust of the earth) ; ![428_Velocity of Longitudinal Wave1.png](https://www.expertsmind.com/../CMSImages/428_Velocity of Longitudinal Wave1.png)
B ¾ Bulk modulus ; η ¾ Modulus of rigidity; ρ ¾ Density.
Newton's Formula: He assumed that when sound propagates through air temperature remains fixed. i.e. the phenomena is isothermal.
k = Eθ = P [Eθ =Isothermal elasticity; P = Atmospheric pressure]
For air at N.T.P. N/m2 and ρ ¾ 1.29 kg/m3.
= 279 m/s
However the experimental number of sound in air is 332 m/sec which is greater than that given by Newton's formula.
Laplace correction: He modified Newton's formula assuming that propagation of sound in gaseous medium is adiabatic process. For adiabatic method
k = EΦ = γP EΦ¾ Adiabatic elasticity γ = Cp/Cv = 1.41
For air, ![212_Velocity of Longitudinal Wave5.png](https://www.expertsmind.com/CMSImages/212_Velocity%20of%20Longitudinal%20Wave5.png)
Relation between velocity of sound and root mean square velocity : If sound travel in a gaseous medium then vsound=√(γRT)/M and r.m.s. velocity of gas vrms=√(3RT)/M
So vrms /vsound = √(3/γ) or vsound= [γ/3]1/2vrms
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