Speed of Sound in Gases

Sound can be contemplated as a longitudinal, mechanical wave and it can traverse through any channel. However, it cannot traverse through the void area. No sound exists in a vacuum. The sound may exhibit variation in pressure. An area of heightened pressure on a sound wave is compression (or condensation) and a region of curtailed pressure on a sound wave is rarefaction (or dilation).

Characteristics of a Sound Wave

• Crest and trough: In a wave, a top is referred to as the crest and a valley is called the trough.

• Wavelength: It is the gap between continuous compressions (C) or two continuous rarefactions (R). It is also represented via λ (Greek letter lambda). Its SI unit is metre (m).

• Frequency: It is represented by means of ν (Greek letter, nu). Its SI unit is hertz (Hz).

• The time period of the wave: it is the time taken to complete one compression and rarefraction.

• It is denoted by T, and the SI unit is second (s).

• Frequency and time period are related as follows:

ν = 1/T

• Pitch: The faster the movement of particles of the source (or object which is producing sound), the higher is the frequency and the higher is the pitch.

• The amplitude of the wave: It is the magnitude of the maximum disturbance (clashing of particles) in the medium on either side of the mean value. It is shown by the letter A. Its unit is the same as distance (metre). 

• The hardness (you can also say loudness) or softness (or you say sweet voice) of a sound is determined by its amplitude. 

• A sound wave spreads out from its source. As it goes far from its source, you will listen to less sound because its amplitude, as well as its loudness, decreases. 

• Quality or timber of sound: It helps to distinguish one sound from another having the same pitch and loudness. 

• The sound, which is more pleasant to hear as compared to others, is said to be of rich quality. 

• A sound of a single (or you can say 1 unit) frequency is called a tone. 

• The pleasant sound produced due to a mixture of several frequencies ( many sounds mixing with each other) is called a note.

• Noise (disturbance) is unpleasant to the ear.

• The intensity of sound: It is the amount of sound energy (number of frequency or the number of cycles that pass through) passing each second through the unit area (or point).

Speed of Sound in Different Media

• Sound propagates (vibrates) through a medium (or object) at a finite speed. 

• The speed of sound depends on the properties of the medium (particular object) through which it travels.

The speed of sound decreases from solid (including metal, non-metal) to gaseous state (air).

Within a medium, the speed of sound increases with an increase in temperature (if you increase temperature, the molecules gain kinetic energy, which makes them collide with each other faster and more impactfully)

Reflection of Sound

The law of reflection of sound describes that the direction in which the sound is incident (touching the object) and reflected (bouncing back after touching the object) make equal angles with the normal (dividing line between incident line and reflected line) to the reflecting surface at the point of incidence, point of reflection, and normal line which lie on the same plane.

Echo: Echo is the reflection (repetition) of sound that arrives at the listener with a delay after the direct sound.

• The sensation of sound is processed and sent to our brain for about 0.1 s.

• To hear an echo easily, the time interval between the original sound and the reflected sound should be at least 0.1s.

• The total distance covered by the sound from the point where it is created to the reflecting surface and back should be at least:

344 m/s × 0.1 s = 34.4 m (here, 344 m/s is the speed of sound)

• For hearing echoes impeccably, the reciprocal distance of the hindrance from the source of sound must be half of this distance, that is,17.2m. 

• This distance changes with the varying temperature of a gas.

• Echoes can be heard more than once due to multiple successful reflections

• The roaring of thunder can be heard due to successful reflection on multiple surfaces.

Doppler Effect Formula

The Doppler effect formula can be used to compute the velocity of the source and observer, as well as the original and observed frequencies of the sound waves. While there is only one Doppler effect formula, it changes based on the observer’s or sound source’s velocities in different scenarios. This is the Doppler effect formula:

f’= f(v + vo)/(v – vs) 

Here, f’ = observed frequency

f = actual frequency

v = velocity of sound wave

vo = velocity of the observer

vs = velocity of the source

Conclusion

Sound waves are characterised by the movement of particles within the medium, which are known as mechanical waves. Sound cannot move through a vacuum because there are no particles to vibrate. Gas is the most common medium through sound travels. While a vibrating object moves in advance, it pushes and compresses the gas within the front of it, developing a location of immoderate stress.