Sound Waves

SOUND WAVES

Sound is always produced by some vibrating body. The vibrating body excites mechanical waves in the surrounding medium. The mechanical waves propagate in the form of a series of compressions and rarefactions in the air and set the ear drum vibrating. It causes a sensation of hearing.

The propagation of sound requires the presence of an elastic medium. Sound cannot travel in a vacuum.

The following points may be noted about sound waves

(i) Sound waves are longitudinal waves. 

(ii) Material medium (solid, liquid or gas) is necessary for the transmission of sound from one place to another. 

(iii) The velocity of sound is greater in solids and liquids than in gases.

Audible and Inaudible Sounds

(i) Those sounds which human ear can hear are called audible sounds. The range of human hearing is 20 kHz to 20 kHz. In other words, we cannot hear sounds of frequency below 20 Hz or above 20 kHz. 

(ii) Those sounds which human ear cannot hear are called inaudible sounds. The sounds of frequency below 20 Hz are called infrasonics while sounds of frequency above 20 Hz are called ultrasonics. Infrasonics and ultrasonics find wide applications in science and engineering.

Velocity of sound in a medium

The velocity of sound in a medium depends upon elasticity and density of the medium. According to Newton's formula, the velocity v of sound is given by

where, E = modulus of elasticity of the medium

ρ = density of the medium.

(i) For solids, E = Y (Young's modulus of elasticity).

......(1)

(ii) For liquids, E = K (Bulk modulus of elasticity).

(iii) For gases, E = K (Bulk modulus of elasticity),

Newton assumed that when sound waves travel through a gas (e.g. air), the compressions and rarefactions are formed so slow that temperature of the medium remains the same.

In other words, the propagation of sound waves in a gas takes place under isothermal conditions. It can be easily shown that under isothermal conditions, bulk modulus of a gas is equal to the pressure of the gas.

Velocity of sound in air by Newton's formula

According to Newton's formula, the velocity v of sound in air is given by:

We know that for air at N.T.P:

P = 0.76 × 13,600 × 9.8 N/m2; ρ = 1.293 kg /m3 

⸫ Velocity of sound in air at N.T.P.

This value is about 16% less than the experimental value (332 m/s) for the velocity of sound in air at N.T.P. This large difference in the two values (experimental and theoretical) cannot be attributed to say experimental error.

In 1817, Pierre Laplace, a French scientist, explained the reason for this discrepancy.

The speed of sound in air is commonly taken as 344 m/s for normal conditions. This is very less compared to the velocity of light.

Table 3.1 gives the speed of sound in some media. Sound travels faster in liquid media than in gaseous media and much faster in solid media.

Table 3.1 Velocity of sound in various media