Question

The velocity of sounds depends on density and modulus of elasticity derive and expression for velocity of sound?

Answer 1

Answer:

The speed of sound is determined by the density and elasticity of the medium in which it travels.

Explanation:

•  In general, sound travels faster through liquids than through gases and faster through solids than through liquids.
• The faster sound travels through a medium, the higher the elasticity and the lower the density.
• Elastic density of medium = d  = mass / length  = M L⁻³
• Coefficient of elasticity E = stress / strain
•           =  [ M L⁻¹ T⁻²   ]
• let velocity v  be =  d^n    E^m
•    so  L¹ T⁻¹  =  M^(n+m)   L^(- 3 n - m )  T^(- 2m)
•  equating the powers of corresponding dimensions
•                 n + m = 0        so n = -m.
•                3 n + m = -1         =>   n = -1/2  and  m = 1/2
• SO the formula  is :    v  = K √ (E / d)          where  K is a constant