Factors Affecting The Speed Of Sound In Gases

What are waves..?

Waves are nothing but the disturbance created at a particular point. Any disturbance sets the periodic motion of a particle in a medium which is then propagated ahead using waves. For example, throwing a stone in a lake causes oscillations in water molecules at the point of contact. These oscillating particles then set the same periodic oscillations in neighbouring molecules, and the disturbance is hence propagated in all directions. The wave transfer only energy and not the matter during propagation. These oscillations or vibrations can be of two types, transverse and longitudinal. 

Sound as a type of wave:

Sound is an example of a progressive, longitudinal wave. A sound wave also called an acoustic wave is set into motion when particles or an object is set into oscillation or vibration. For example, in the vocal cord in the human throat, tuning fork, a string of a guitar, etc., the vibrations set at the point of disturbance set periodic patterns of compression and rarefaction in the connecting molecules of the medium. For propagation of these waves, two molecules must contact each other for the transfer of energy and vibration in the forward direction. Thus sound waves require some medium, like air or water, and hence categorized as mechanical waves. 

Like other waves, sound waves are described with the help of different characteristic parameters. These include the following terms-

• Amplitude:

In sound waves, since they are longitudinal waves, the vibrational motion of particles of the medium is definite to and fro motion of particles about their original mean position. The maximum distance covered by the vibrating particle in either direction is known as the amplitude of the wave. Each molecule of medium propagating the sound wave has equal amplitude. Amplitude is measured in meters in the SI system. 

• Period (T):

The time taken by one particle to complete one vibration is known as a period. SI unit of a period is second. 

• Frequency (n):

The number of vibrations completed by a particle in the time of one second is called the frequency of the sound wave. For sound waves, the SI unit of frequency is hertz (Hz).

• Wavelength (λ):

The distance between two consecutive compression or rarefactions is known as the wavelength of the sound wave. 

• Velocity (v):

The distance covered by the wave in one second is called the velocity of the sound wave. 

Propagation of sound waves in the air and their velocity:

As stated earlier, for the sound wave to be propagated, it requires some medium. Most of the time, the medium for the propagation of the sound wave is air, a mixture of gases. Hence it is important to study the characteristics, parameters, and speed of a sound wave in gases. Also, it is critical to study the effects of different conditions on the speed of a sound wave. 

The speed of the sound wave in the air is generally studied with the help of prior work done and formulae stated by Newton and Laplace.  The general speed of the sound wave in air is given as-

v= √E ⁄ P

E is the modulus of elasticity of the medium, and is the density of the medium. 

Laplace proposed that the compression and rarefaction during the propagation of sound waves follow the adiabatic process, and hence, the elasticity of modulus also should be considered accordingly. Thus he stated that E would be the adiabatic modulus of elasticity of air which is equal to the product of specific heat of air at constant pressure (γ) and pressure of the air. Thus the speed of a sound wave will be as

v= √γP⁄ P

The specific heat of air is 1.41. Thus at standard temperature and pressure conditions (NTP), the speed of a sound wave in the air will be equal to 332.2m/s. 

Now we will try to understand the effect of pressure and density of the air on the speed of propagating sound waves.

• Effect of pressure change:

We know that density is equal to the ratio of mass to volume. Hence substituting this ratio for the density term in the formula, the speed of the sound wave is

v= √γPV ⁄ M

For an ideal gas, according to Boyl’s law, at constant temperature value of PV is also constant. This implies that if the temperature of the air is constant, then changing the pressure of the air column will not have any effect on the speed of the sound wave.

• Effect of temperature of the air:

Though changes in pressure alone of air do not have any effect on the velocity of the sound wave, it is not the same for changing the temperature of the air. Change in the temperature of the air eventually leads to changes in the density of air. As temperature rises, the density of air decreases. The speed of the sound wave is inversely proportional to the square of the density of air. Hence decrease in density as an effect of temperature rise will increase the speed of the sound wave. In other words, increasing the temperature of the air will increase the speed of the sound wave in proportion to the square root of the absolute temperature of the air. 

This also describes the effect of change in density in the air leading to a decrease in the speed of the sound wave. 

Conclusion:

Sound is nothing but a type of wave. Sound waves are characterized as mechanical, longitudinal progressive waves. Since these are mechanical waves, the presence of a medium is a prerequisite for the propagation of the sound wave. The various parameters associated with sound waves like wavelength, amplitude, frequency, and, most importantly, velocity depend on the nature and physical parameters of the medium. The velocity of the sound wave in the air has been widely studied and described by Newton and Laplace.  At constant temperature, a change in pressure of the air does not affect the speed of the sound wave. On the other hand speed of the sound wave is directly proportional to the square root of absolute temperature and inversely proportional to the square root of the density of the air.