Speed Of Sound Formula

The speed of sound is defined as the travelled by the sound wave that propagates per unit time through an elastic medium. In a perpendicular medium, the speed of the sound depends on the elasticity and density of the medium. If the speed of the sound is greater then the elasticity is more and density is less.

The formula of the speed of sound formula is expressed as

\(\begin{array}{l}c = \sqrt{\gamma \times \frac{P}{\rho }}\end{array} \)


P = pressure

ρ = density

γ = Ratio of specific heat.

Example 1

The sound wave with density o.o43 kg/mand pressure of 3kPa having the temp 30C travels in the air. Find out the speed of the sound?



Temperature T = 276 K

Density ρ = 0.043 kg/m3

Pressure p = 3kPa = 3000 Pa

The ratio of specific heat in air = 1.4

The formula for speed of sound is

\(\begin{array}{l}c = \sqrt{\gamma \times \frac{P}{\rho }}\end{array} \)

c = √[γ×(P/ρ)]

c  = √[1.4× (3000 / 0.043)]

Therefore, speed of sound = 312.52 m/s


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