# Speed Of Sound Formula

## Speed of Sound Formula

Any medium can transmit the vibration or disturbance known as sound. When it reaches a person’s ear, it is audible and moves by transferring energy from one particle to another. For instance, when an object vibrates, energy is transferred to the nearby particles, which causes them to vibrate as well. The lack of particles that could serve as a medium prevents sound from travelling through the vacuum. Only a medium like water, air, or a solid can transmit sound. This article will talk about sound waves and the Speed of Sound Formula.

### Speed of Sound Formula

A longitudinal wave, sound travels through air and liquids but travels both longitudinally and transversely through solids. The properties of the medium in which a sound wave is propagating determine how quickly it moves through that medium. Its speed is independent of the wave’s properties or the force that created it. Its propagation through a medium can be used to examine some of that medium’s characteristics.

The distance a sound wave travels in one unit of time while propagating through an elastic medium is known as the speed of sound. The density and elasticity of a given medium affect the speed of sound in that medium. Physics states that as the sound wave speed increases, elasticity increases, density decreases, and vice versa. As a result, solids have the highest and lowest sound speeds.

The Speed of Sound Formula is a crucial part of the syllabus for students, and they need to be thorough with the concept. The concept of Speed of Sound Formula can be tricky for students to comprehend. The concept can be understood with the help of the textbooks, but they might not seem enough for some students. They can require more resources to have a good understanding of the Speed of Sound Formula.

### What is a sound wave?

The speed of sound can be computed as,

speed of sound = the square root of (the coefficient ratio of specific heats × the pressure of the gas / the density of the medium).

Mathematically,

c =(√γ×Pρ)

Where,

c Speed of sound

P Pressure

ρ Density

γ Specific heat ratio

Here γ is representing the adiabatic index and also known as the isentropic expansion factor. It is computed as the ratio of specific heats of a gas at a constant pressure to a gas at a constant volume.

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### Solved Examples

Q.1: The sound waves travel in the air with a density of 0.034 kg/m³ and pressure of 2k Pa with a temperature of 2°C. Calculate the speed of the sound.

Solution:

As given here:

Temperature, T = 2° C

Density, ρ=0.034kg/m³

and, pressure P = 2k Pa

i.e. P = 2000 Pa

as we know that specific heat ratio in air is,

γ=1.4

Now the speed of sound formula is given by

c =(√γ×Pρ)

c =(√1.4×20000.034)

c= (√82352.94)

c = 286.97

Therefore, speed of sound = 286.97 m/s.

Q. 2: Find out the pressure if sound travels through a medium having a density 0.05 KPa and speed of sound is 400 m/s.

Solution:

As given in the problem,

Density, ρ = 0.05 KPa,

Speed of sound, c = 400 m/s

Also, γ = 1.4 at room temperature for gases.

Now the speed of sound formula is:

c =(√γ×Pρ)

rearranging the formula,

P = c2×ργ

P = 4002×0.051.4

P= 1600×0.051.4

P= 5714.28 Pa

Therefore, Pressure will be 5714.28 Pa.