Sound-

 

Sound is a form of energy which produces in us the sensation of hearing.

 

It is emitted by a vibrating source such as-

• a guitar string
• human vocal cords
• prongs of a tuning fork
• diaphragm of a loudspeaker etc

 

Sound Wave-

 

The waves which carry sound energy are called as sound waves.

 

Sound is a mechanical three dimensional and longitudinal wave.

• Being a mechanical wave, it needs a material medium having properties of inertia and elasticity for its propagation.
• Being a longitudinal wave, it propagates in any medium through a series of periodic compressions and rarefactions of pressure.

 

Important Note The formation of transverse waves is possible only when the medium possesses the elasticity of shape. Since solids alone possess the elasticity of shape, therefore, sound can travel through solids in the form of transverse waves. However, solids, liquids and gases, all possess volume elasticity. Therefore, longitudinal waves can be transmitted through all the three states of matter. Thus, sound is carried by the longitudinal waves through fluids (liquids and gases).

 

Equation of a Sound Wave (Longitudinal Wave)-

 

A longitudinal mechanical wave can be described in two ways-

1. Displacement wave form
2. Pressure wave form

 

Displacement Wave Form-

 

• As the sound wave propagates in a fluid medium, the particles of the medium oscillate along the direction of wave propagation.
• When a sound wave is described in terms of longitudinal displacement suffered by the particles of the medium, it is called a displacement wave.

 

A sound wave propagating in x-direction can be given as-

where-

s = displacement of oscillating particle from its mean position

s_o = amplitude of oscillation

 

NOTE-

• We are denoting the displacement of medium particles by letter ‘s’ instead of letter ‘y’ so as to avoid getting confused about the direction of oscillation.
• As wave propagates in x-direction, particles also oscillate along x-direction.

 

Pressure Wave Form-

 

• As the sound wave propagates in a fluid medium, the particles of the medium come closer or move away from one another.
• As a result, the pressure of the medium changes.
• The change in pressure can also be regarded as a measure of disturbance at a point.
• When a sound wave is described in terms of excess pressure generated due to compression and rarefaction, it is called a pressure wave.

 

A sound wave propagating in x-direction can be given as-

or simply,

where-

• P or ΔP = change in pressure or pressure in sound wave
• P_o or ΔP_o = ABK called amplitude of pressure wave or pressure amplitude (i.e. maximum change in pressure at a point)
• A = displacement amplitude
• B = bulk modulus of the medium
• K = propagation constant

 

Important Note From displacement and pressure wave forms, we infer that displacement wave and pressure wave have a phase difference of π/2 between them. When displacement at a location is minimum, the change in pressure is maximum and vice-versa.

 

Test Your Concepts-

Equation of Sound Wave

 

Next Article-

Speed of Sound Wave in Fluid

 

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