A wave is a vibratory disturbance in a medium which carries energy from one point to another point without any actual movement of the medium. There are three types of waves:
A wave in which the particles of the medium vibrate at right angles to the direction of propagation of wave is called a transverse wave.
These waves travel in the form of crests and troughs.
A wave in which the particles of the medium vibrate in the same direction in which the wave is propagating is called a longitudinal wave.
These waves travel in the form of compressions and rarefactions.
Sound waves of all the mechanical waves that occur in nature, the most important in our everyday lives are longitudinal waves in a medium, usually, air, called sound waves.
Sound waves are mechanical longitudinal waves and require medium for their propagation.
[sound waves cannot propagate through vacuum.
If Vs, Vi and Vg are speed of sound waves in solid, liquid and gases, then
Vs > Vi > Vg
Sound waves (longitudinal waves) can reflect, refract, interfere and diffract but cannot be polarised as only transverse waves can polarised.
Velocity of longitudinal (sound) wave in any medium is given by
where E is the coefficient of elasticity of the medium and ρ is density of the medium.
According to Newton, the propagation of longitudinal waves in a gas is an isothermal process. Therefore, velocity of longitudinal (sound) waves in gas should be
where ET is the isothermal coefficient of volume elasticity and it is equal to the pressure of the gas.
According to Laplace, the propagation of longitudinal wave is an adiabatic process. Therefore, velocity of longitudinal (sound) wave in gas should be
where, ES, is the adiabatic coefficient of volume elasticity and it is equal to γ p.
(i) Effect of Pressure: The formula for velocity of sound in a gas.
Therefore, (p/ρ) remains constant at a constant temperature.
Hence, there is no effect of pressure on velocity of longitudinal wave.
(ii) Effect of Temperature: Velocity of longitudinal wave in a gas
Velocity of sound in a gas is directly proportional to the square root of its absolute temperature.
If v0 and vt are velocities of sound in air at O°C and t°C, then
(iii) Effect of Density: The velocity of sound in gaseous medium
The velocity of sound in a gas is inversely proportional to the square root of density of the gas.
(iv) Effect of Humidity: The velocity of sound increases with increase in humidity in air.
If speed of a body in air is greater than the speed of sound, then it .s called supersonic speed. Such a body leaves behind it a conical region of disturbance which spreads continuously. Such a disturbance is called a shock wave.