Speed of a sound wave, \(v = \sqrt{\dfrac B \rho }\), where

v = velocity

B = Bulk modulus of the material.

ρ = normal density of the fluid

Hence the velocity of a longitudinal wave in a medium depends on its elastic properties and inertial properties of the medium.

Newton’s formula for speed of sound in a gas

v = √(P/ρ)

The density of air at temperature 0°C and pressure 76 cm of mercury column is ρ = 1.293 kg/m³

So P = .76m*(13.6*10^3 kg/ m³)*(9.8 m/s²) = 101292.8

Hence P/ ρ = 78339.37 √(P/ρ) = 279.8917 m/s

The velocity of sound in air comes as 280 m/s.

But the measured value of speed of sound in air is 332 m/s

Laplace's correction

Laplace suggested a correction. With Laplace’s correction the formula is

v = √( γ P/ρ)

where γ = Cp/Cv (Cp and Cv are molar heat capacities at constant pressure and constant volume respectively)

With this new formula the value comes out to be 331.1723 closer to 332 m/s.

Effect of pressure, temperature and humidity on speed of a sound wave

The speed of sound is not affected by the change in pressure provided the temperature is kept constant. If pressure is changed but the temperature is kept constant, the density varies proportionately and P/ρ remains constant.

Speed of sound increases with increasing humidity. The density of water vapour is less than dry air at the same pressure. Thus, the density of moist air is less than that of dry air.

Intensity of sound waves

The intensity of a sound wave is defined as the average energy crossing a unit cross sectional area perpendicular to the direction of propagation of the wave in unit time.

The loudness of sound that we feel is mainly related to the intensity of sound. It also depends on the frequency to some extent.

Appearance of sound to human ear

The appearance of sound to human ear is characterised by three parameters.

- pitch
- loudness
- quality

Note:

- Pitch: Higher the frequency, higher will be the pitch.
- Loudness: Loudness that we sense is related to the intensity of sound though it is not proportional to it.
- A sound generated by a source contains a number of frequency components in it. Certain sounds have well defined frequencies which have considerable amplitude. Such sounds are particularly pleasant to the ear.

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