Speed of Sound

The speed of sound is is the distance traveled in a unit of time by a sound wave through an elastic medium, and is usually given as 344 m/s.

Learning Objective

Calculate the speed of sound from the properties of the media

Key Points

Sound can travel through any compressible material. These media can be solid, liquid, gas, or even plasma.
The speed of sound is dependent on the properties of the material it travels through. It will travel faster through a solid than a liquid, and faster through a liquid than a gas.
The general number given for the speed of sound is calculated at sea level, in air, at normal atmospheric pressure. That value is 344 m/s.

Terms

elasticity
The property by virtue of which a material deformed under the load can regain its original dimensions when unloaded
kelvin
in the International System of Units, the base unit of thermodynamic temperature; 1/273.16 of the thermodynamic temperature of the triple point of water; symbolized as K

Full Text

Speed of Soud

The speed of sound is is the distance traveled in a unit of time by a sound wave through an elastic medium. This medium can be a solid, liquid, gas or even plasma. The speed of sound is dependent on the properties of the media the sound is travelling through. The general value given for the speed of sound is the speed of a sound wave in air, at sea level, at normal atmospheric pressure; that number is 344 m/s. However, this number is not constant. Sound travels faster in a solid than in a liquid, and faster in a liquid that in a gas.

Types of Sound Waves: Compression and Shear

There are two different kinds of sound waves: compression waves and shear waves. Compression waves can travel through any media, but shear waves can only travel through solids. The speed of a compression wave is determined by the media's compression capacity, shear modulus, and density, while the speed of the shear wave is only determined by the shear modulus and density. The shear modulus is a measurement of the elasticity or rigidity of a material. Calculating this is outside of the scope of this atom, but there are tables which tell you its value for materials.

Calculating the Speed of Sound

The speed of sound is usually denoted by $c$, and a general equation can be used to calculate it. This is called the Newton-Laplace equation:$c=\sqrt{\frac{K}{\rho}}$K is the coefficient of stiffness, and p is the density of the media. From this equation, it is easy to see that the speed of sound will increase with stiffness and decrease with density. This is a very general equation, there are more specific derivations, for example:

The speed of sound in air at sea level is given by the following equation:$c_{air}=331\frac ms*\sqrt{\frac{T} {273K}}$ T is the temperature in Kelvin.

Mach Number

You may have heard the term Mach number in relation to speed of space craft or jets before. This is a ratio of an object's speed in relation to the speed of sound. The Mach number is given by the following, dimensionless equation:$M=\frac va$M - Mach numberv - Velocity of object a - Speed of sound in medium. If something is travelling at the speed of sound, that would make the equation equal to 1, and can be denoted as Mach 1. shows a jet that is travelling at the speed of sound or faster. The vapor cone is made just before it reaches the speed of sound and is caused by a sudden drop in air pressure.

Faster than the Speed of Sound

This is a jet that is just about to break the sound barrier.

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