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Speed of Sound Formula

The speed of sound is defined as the distance travelled by a sound wave propagating through an elastic medium per unit time. The speed of sound in a particular medium depends on density and elasticity of a medium. More is the speed of sound greater is the elasticity and smaller is the density. The speed of sound is maximum in solids and minimum in solids.

The speed of sound formula is given by,


P = pressure

ρ = density

γ = specific heat ratio.

Example 1

The sound waves travels in the air with a density of 0.034 kg/m3 and pressure of 2kPa having temperature of 2o C. Calculate the speed of the sound.



Temperature T = 275 K,

Density ρ = 0.034 kg/m3,

Pressure p = 2kPa = 2000 Pa

The speed of sound formula is given by

c = γ×Pρ

   = √1.4×2 / 0.034k

Therefore, speed of sound = 286.97 m/s.

Example 2

Calculate the pressure if sound travels through a medium that has a density 0.05 kPa and speed of sound is 400 ms-1.



Density ρ = 0.05 kPa,

Speed of sound c = 400 ms-1

Pressure is given by the formula,

P = c2ρ / γ

= 4002×0.05 / 1.4

Therefore, Pressure = 5714.28 Pa.