Sound Wave Formulae for NEET

A sound is a vibration that propagates through a medium in the form of a mechanical wave. The medium in which it propagates can either be a solid, a liquid or a gas. Sound travels fastest in solids, relatively slower in liquids and slowest in gases.

Longitudinal displacement of the sound wave

y = A sin (ωt – kx)

1.Speed of Sound

\(C = \sqrt{(\gamma \times P)/\rho }\)

Where P = Elastic modulus for the medium

ρ = density of the medium

γ = radio of specific heat

2. Loudness of sound

L = 10 log10(I/I0) dB

I0 = the minimum intensity human ear can hear

 I = intensity at a distance r from the point source

3. Open organ pipe

The frequency of the pth overtone is (p + 1)n1

where nis the fundamental frequency

The frequency of harmonics are in the radio 1:2:3….

4. Closed organ pipe

The frequency of the pth overtone is (2p+ 1)n1

where nis the fundamental frequency

The frequency of harmonics are in the radio 1:3:5….

5. Beat frequency

Beat frequency \(f_{b}=\left | f_{2}-f_{1} \right |\)

Where, f1 and f2 are the frequency of the two waves

6.Doppler Effect

The observed frequency f’ = f (v-v0/v-vs)

Apparent wavelength λ’ = λ ((v-vs/v)