Name: The Speed of a Travelling Wave
Uploaded: 2019-07-19
Duration: 4 min 21 s
Description: How do you derive the wave speed of the travelling wave, and what is the relation of the wave speed with wave frequency, wavelength and time period? Let's le...

Question

Explain newton's formula for velocity of sound. What are its limitations?

Accepted Answer

Newton suggested that sound wave when travel in a medium, its velocity depends upon two factors

a) elasticity of the medium $E$ (for fluids it is equal to bulk modulus B)

b) density of medium $ρ$

Using the basic concepts of dimensional analysis the speed of sound in a medium was given by $\sqrt{\frac{E}{ρ}}$

Newton proposed that the propagation of sound wave in a medium such as air is isothermal in nature.

Using ideal Gas equation $P V = n R T$ .....(i)

Using partial differentiation of equation (i)

$P d V + V d P = 0$ (by product rule of differentiation)

$P = - V d P / d V$

Now as we know bulk modulus, $B = - V d P / d V$

Now as $P = B =$ Elasticity

Hence, formula reduces to $V = \sqrt{P / ρ}$

Newton worked on the propagation of sound waves through the air. He assumed that this process of propagation is isothermal. Absorption and release of heat during compression and rarefaction will be balanced, thus, the temperature remains constant throughout the process.

The limitation of the formula was that the velocity of sound obtained from Newton's equation did not match with the actual speed of sound in air and his formula was later corrected by Laplace who suggested that the motion of sound through air is an adiabatic process.

Explain newton's formula for velocity of sound. What are its limitations?

Important Questions on Sound

Learn and Prepare for any exam you want !