# Speed of Sound Propagation

## Introduction

Sound waves are essential to human life, as they are vital in countless aspects of life, such as they are primarily in the dissemination of information.

Sound waves are applied in several areas, such as in navigation, tracking of ships, and aircraft with the help of sonar, a device for detecting sound waves. These devices are useful in conducting effective communications.

In the field of entertainment too, sounds are used in cassettes, radio and many more. However, it needs to be noted that during the propagation of the sound waves, the waves get reflected, refracted and as well as attenuated by the respective medium.

## What is sound?

Sound waves can be referred to as the kind of energy that is generated through the notion of vibrations. While conducting such vibrations, the sound waves lead to vibrations of other molecules of air present within their surroundings.

This is because the vibration of the molecules of the sound waves tends to force into the molecules that are in close vicinity and thereby these particles of sound waves propagate through the respective medium (Bohlen et al. 2020).

It is to be noted that without the presence of any medium, the propagation of sound waves is not possible.

## Characteristics of sound

Sound waves form several peaks and valleys that are continuous in nature. The distance that is formed from the covering of the two of these continuous troughs or peaks'' is known as the wavelength of the particular wave.

However, the frequency is determined by the number of cycles that are formed under a particular unit of time (Ville et al. 2018).

The sound waves have amplitude, time period and velocity and speed and these support in stating the nature of sound waves. The distance that is minimum, in which the waves of sound tend to repeat it is determined as wavelength.

Figure 1: Sound waves

## Definition of speed of sound and its mathematical expression

The speed of sound refers to a propagation which is dynamic in nature for waves that takes place through various mediums. However, it is denoted that the sound while travelling through different mediums tends to vary in their speed (Pages.jh, 2022). While talking about the speed of sound it needs to be considered that the speed of sounds is always calculated when travelling in an elastic medium.

The mathematical expression for the speed of sound in the gaseous medium is, 𝜈 = √ 𝛾 P/ 𝜌, where, 𝜈 is determined as the speed of sound, P denotes the pressure within the gaseous medium. 𝛾 is known for being the coefficient of adiabatic expression and lastly, 𝜌, represents density of medium, where sounds travel.

Figure 2: Speed of sound waves

## Examples of propagation of sounds

Several examples of propagation of sounds are found in our day-to-day life, such as a fan for fan of air conditioning, taking off aeroplanes, buzzing of bees, and the popping of balloon (Sfu, 2022). In the field of physics, sound waves are used in detecting the location of submarines, aircraft, and many more.

Figure 3: Speed of sound waves

## Factors that affect the speed of sound

The factors that intend to affect the speed of sound are the notions of the temperature and density for the respective medium. While sound waves travel from one medium to another, the density of the respective medium tends to affect the speed, as it is directly proportional to each other (Sciencedirect, 2022). Therefore, it means, the speed will be higher within a medium of high densities. This speed is also directly proportional to the temperature, as, with a high temperature, the sound seems to travel at a faster rate.

## Speed of sound in different media

In solid medium, the speed of sound is high, with respect to other mediums and it is approximately, 6000 m/s, due to high density. However, the speed of sound is quite lower in liquids and gasses and in a vacuum; sound waves do not travel.

## Conclusion

In this tutorial, it is noticed that the sound wave is a necessary aspect that is vastly applicable in our daily lives. However, due to the unique characteristics of nature of sound waves several occurrences such as the stringing of the guitar are noticed to explain its generation of sound waves. However, density and temperature plays an important role in determining the factors affecting the speed of sound.

## FAQs

Q1. What is defined as the intensity of sound?

Intensity of sound is determined by the amount of energy that passes through the point having unit area. However, the intensity of sound is inversely proportional to the square of distances that is acknowledged between the source and that of the point the sound waves pass through. Moreover, the intensity of sound is directly proportional to the square of frequency as well as vibrations of the medium. Hence it is also directly proportional to the density of the respective medium.

Q2. What property is applicable for distinguishing the sharp and dull sounds?

The notion of pitch property is best applicable in the segregation of the distinction between the dull and sharp sounds. This is because the pitch depends on the frequency associated with sound waves, which are directly proportional to each other. This means that with the high frequency the pitch will also increase.

Q3. What are the factors that affect the speed of sound in the gaseous medium?

The factors that are responsible for affecting the speed of sound in a gaseous medium are aspects of elasticity and density of the respective medium. However, it is to be noted that the speed of sound depends highly on the notions of composition and temperature of the medium. In the medium of air, the behaviour of sound waves tends to deflect due to dependency on frequency and pressure associated with normal air.

## References

### Journals

Bohlen, M., Sobirey, L., Luick, N., Biss, H., Enss, T., Lompe, T., & Moritz, H. (2020). Sound propagation and quantum-limited damping in a two-dimensional Fermi gas. Physical Review Letters, 124(24), 240403. Retrieved from: https://journals.aps.org

Ville, J. L., Saint-Jalm, R., Le Cerf, É., Aidelsburger, M., Nascimbène, S., Dalibard, J., & Beugnon, J. (2018). Sound propagation in a uniform superfluid two-dimensional Bose gas. Physical Review Letters, 121(14), 145301. Retrieved from: https://journals.aps.org

Websites

Pages.jh, (2022), Vibrations, Retrieved from: https://pages.jh.edu [Retrieved on 17th June 2022]

Pressbooks-dev.oer.hawaii, (2022), The speed of sound, Retrieved from: http://pressbooks-dev.oer.hawaii.edu/ [Retrieved on 17th June 2022]

Sciencedirect, (2022), Sound propagation, Retrieved from: https://www.sciencedirect.com/ [Retrieved on 17th June 2022]

Sfu, (2022), Speed of sound, Retrieved from: https://www.sfu.ca/ [Retrieved on 17th June 2022]

Tutorialspoint

Simply Easy Learning