Velocity of Sound Wave in Gas
Newtons formula is first derived by sir lssac Newton. Sound wave is a mechanical longitudinal that can propagate through through air medium in the form of alternate compression and rarefaction.
In the region of compression heat is evolved and heat is absorbed in the reason of refraction. So, heat developed in compression region can be easily transferred to the reason of rarefraction.As a result , the temperature of gas remain unchanged.
From this above fact, Newtons assume that the propagation of sound wave in air is isothermal process.then,the velocity of sound in air medium can be written as,
V = √(Kiso/d) ……….1)
,where Kiso = Isothermal bulk modules of elasticity of air
d = density of air
The equation of state for isothermal change is,
PV = constant ……….2)
Differentiating equation 2 with respect to ‘T’
d(PV)/dT = 0
or, PdV/dT + VdP/dT = 0
or, p = -dP/(dV/V)
or, P = -Stress/strain
or, P = Kiso ………….3)
Negative sign inducates increase in pressure, decrease in volume and vice versa.
From equation 1 & 2, we get
V = √(P/d)
Hence, This is required exoression of newton’s formula for velocity of sound wave in gas.