10.3 - Sound Needs a Medium for Propagation

Sound is a type of mechanical wave that travels through a medium. It cannot travel through a vacuum because it requires particles to propagate. The medium could be any form of matter, whether solid, liquid, or gas. In this section, we will discuss why sound needs a medium and how it propagates through different types of media.

What is a Medium?
A medium is any substance or material that carries the sound wave. The medium consists of particles, such as molecules in air or atoms in solids, which vibrate when sound waves pass through them. These vibrations are transferred from one particle to the next, allowing sound to propagate.

Propagation of Sound:
When a sound wave is produced, the particles in the medium vibrate. These vibrations cause a series of compressions (high-pressure regions) and rarefactions (low-pressure regions) that travel through the medium. The transfer of energy from one particle to another causes the sound to travel. The speed of sound varies depending on the medium it is traveling through.

Why Sound Cannot Travel in a Vacuum:
In a vacuum, there are no particles to transmit the vibrations. Sound cannot travel because it requires a medium to carry the vibrations from one particle to the next. Therefore, in outer space, where there is no air or any other medium, sound cannot propagate, and it is "silent."

Speed of Sound in Different Media:
The speed at which sound travels depends on the properties of the medium, such as its density and elasticity. For example, sound travels faster in solids than in liquids and gases. This is because the particles in solids are closer together and can transmit the vibrations more quickly. In contrast, in gases, the particles are spread out and it takes longer for the vibrations to pass from one particle to another.

The speed of sound ($v$) in a given medium can be calculated using the formula:

Formula:
$v = \sqrt{\dfrac{B}{\rho}}$

Where:

• $v$ = Speed of sound in the medium (in meters per second)
• $B$ = Bulk modulus (a measure of the medium's elasticity)
• $\rho$ = Density of the medium (in kilograms per cubic meter)

Speed of Sound in Air:
In air, the speed of sound is approximately 343 m/s at room temperature (20°C). However, this speed can change depending on the temperature of the air. As the temperature increases, the molecules in the air move faster, and sound can travel more quickly.

Effect of Temperature on Speed of Sound:
The speed of sound increases with an increase in temperature because warmer molecules in the air are able to transfer the vibrations more quickly. The relationship between the temperature of air ($T$ in Celsius) and the speed of sound ($v$) is approximately given by the formula:

Formula:
$v = 331 + 0.6T$

Where:

• $v$ = Speed of sound in air at temperature $T$
• $T$ = Temperature in Celsius

Sound in Water and Solids:
In water, sound travels faster than in air because water is denser and less compressible. In solids, sound travels even faster because the particles are tightly packed and can transmit the vibrations quickly. For example, the speed of sound in water is about 1500 m/s, and in steel, it is around 5000 m/s.