Explain Newtons formula for velocity of sound. What is its limitation?
Answers
According to Newton, when sound waves propagate in air, compression and rarefaction are formed. He assumed that the process is very slow and the heat produced during compression is given to surrounding and heat loss during compression is gained from surrounding. So the temperature remains constant and sound waves propagate through an isothermal process.
Derivation of Newton's Formula
According to gas law (Boyle's law),
PV = constant
where, P = pressure
V = volume of air
Differentiating above equation, we get
Differentiation of Boyle's Law
where, B is the bulk modulus of the air.
If B is the bulk modulus of the air, v is velocity and ρ is the density, then, velocity is given by:
Relationship of velocity or air with bulk modulus and density
This is the required expression for velocity of sound in air.