Speed of Sound: How Fast Is It? More Than Speed of Light!!

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SOUND

Sound, a type of energy, moves through vibrations in a medium like air, water, or solid materials. When an object vibrates, it generates pressure waves that we hear as sound. These waves can differ in frequency and amplitude, leading to various pitches and volumes. Sound is essential for communication, music, and environmental awareness, impacting our daily lives and interactions with the world.

Definition: Sound is a type of energy emitted by vibrating objects that propagates in the form of waves through an inert medium and produces a sense of hearing in the ears of most animals, including humans.

TYPES OF SOUND WAVE

Subsonic waves: Sound waves whose frequency is less than 20 Hz are called subsonic waves. This wave can be caused by the vibration of very large sensors. Waves produced by earthquakes are an example of a subsonic wave.
Ultrasonic waves: Sound waves whose frequency is higher than 20000 Hz are called ultrasonic waves. The bat creates these waves on its face while flying. If there is an obstacle in front, this wave is reflected by that obstacle. Bats sense the location of obstacles by listening to reflected waves.

SPEED OF SOUND

Sound takes some time to travel any distance, i.e. sound has definite speed. It is easily understood by comparing it with the speed of light. In many everyday occurrences light and sound originate simultaneously. Because the speed of light is so high (about 186,000 mi or 300,000 km per second), it reaches the eyes of a distant observer almost instantaneously. However, since the speed of sound is relatively low, it takes a little longer to reach the ear. That’s why 1. A few moments after seeing the lightning in the sky, the sound of the clouds is heard, 2. The sound of a fast-moving jet plane is almost invisible before it comes overhead, but after it passes overhead, the sound remains for a while.

The speed of sound in air at 0°C is about 332 m/s. This velocity increases as temperature increases, other physical conditions also affect the speed of sound.

EFFECT OF AIR FLOW

The speed of sound changes when the particles themselves move through the medium through which sound propagates. As such, airflow clearly affects the speed of sound. Let us assume that the actual velocity of sound in a given direction = V, the velocity of air flow = v and the angle between the direction of sound propagation and the direction of air flow = θ. Then the component of wind velocity in the direction of amplitude = vcosθ. In this case effective velocity of sound = V + vcosθ.

Special Case:

If the airflow is in the direction of propagation of sound, θ = 0; cos θ = 1. So, in this case effective velocity of sound = V + v.
If the airflow is opposite to the propagation of sound, θ = 180°; cos θ = -1.
If the direction of airflow is perpendicular to the direction of propagation of sound, θ = 90°; cosθ = 0;

So, in this case effective speed of sound = V = its actual speed.

SPEED OF SOUND IN A MATERIAL MEDIUM

The speed with which a sound wave propagates through an inert medium depends on two properties (density and elasticity) of the medium:

Density: If the density of a medium is low, when a vibrating object exerts pressure on that medium, the effect of that pressure can travel over a long distance in a short time. On the other hand, if the density of the medium is high, the pressure effect travels a relatively short distance in the same time. This results in a longer length of condensation and rarefraction caused by low density and thus a higher speed of sound.
Elasticity: A vibrating object exerts a force on the medium. This force causes elastic strain in the medium. The compressed layer expands due to elastic strain. Compressed layers of a medium with high elasticity expand very quickly, while stretched layers also contract very quickly. That is, it takes very little time for condensation to convert to rarefraction or rarefraction to condensation. As a result, the speed of sound in the medium also increases.

Scientist Newton showed theoretically that the speed of sound through medium,

c = √E/ρ. (where, ρ = density of the medium, E = coefficient of elasticity of the medium).

Values of speed of sound in different media (normal pressure and temperature of gaseous media are mentioned)

Medium	Speed of Sound (m/s)	Medium	Speed of Sound (m/s)
Air (0°C)	331	Water (4°C)	1436
Air (20°C)	343	Copper	3970
Oxygen (0°C)	317	Distilled water (25°C)	1496
Hydrogen (0°C)	1286	Steel	4700 – 5200
Carbon dioxide (0°C)	257	Glass	4000 – 5000

SPEED OF SOUND IN A GASEOUS MEDIUM

Air or any other gaseous substance is a type of material medium. So, the formula for speed of sound described in the previous section applies to gases as well. Since the gas has no length or shape, its only elastic coefficient is the bulk modulus. So, if the density of a gas medium is ρ, the bulk modulus is k and the speed of sound through the gas is c,

c = √k/ρ ………(1)

Newton's Calculation

Newton assumed that the mode of propagation of sound through a gaseous medium is the isothermal process. That is, during the propagation of sound, the pressure and volume of different parts of the gas medium may change due to condensation and rarefraction, but the temperature of the gas medium remains constant.

Let us assume that the pressure and volume of a certain amount of gas in a gas medium are p and V respectively. During sound expansion the pressure increases as p + p₁ and hence the volume of the section decreases as V – v. If the temperature is constant, according to Boyle’s law, it can be written,

Proof With Calculas

According to Boyle’s law, pV = constant. Calculating, we get,

To understand how accurate this formula is, the speed of sound through air can be calculated using this formula. Density of air at STP = 0.001293 gm/cm³ and standard pressure = 76 cm Mercury pressure = 76 X 13.6 X 980 dyn/cm². Substituting these values gives,

c = 28000 cm/s = 280 m/s (approx.)

But various experiments show that the speed of sound in air at 0°C is about 332 m/s. From this it can be concluded that Newton’s theory with which he determined the direction of sound in a gas medium must have had a major flaw.

Laplace's Correction

Scientist Laplace first stated that the temperature of a gas does not remain constant during the propagation of sound through a gas medium. Propagation of sound through a gas is a uniform thermal process—Newton’s assumption is incorrect. Laplace postulates that the contraction and expansion of gaseous layers during condensation and rarefraction is so rapid that the temperature of the gas cannot remain constant; since the thermal conductivity and radiation capacity of the gas is very low, heat exchange does not take place between different parts of the gas in that short time. As a result, the temperature of the gaseous layers decreases during the propagation of sound. That is, sound propagation in gaseous medium is an adiabatic process, not an isothermal process.

As the pressure-volume relationship of gas in isothermal process is pV = constant (Boyle’s law), so in constant temperature system the relationship is pV^γ = constant.

Here, γ = C_p/C_v

C_p = specific heat at constant pressure

C_v = specific heat in constant volume

Let us assume that initial pressure = p and initial volume = V of a certain amount of gas. During sound expansion the pressure increases as p + p₁ and the volume decreases to V – v. So,

Proof With Calculas

The relationship between the pressure and volume of a gas in adiabatic system is, pV^γ = constant. Calculating, we get

For air at STP, γ = 1.4, p = 76 X 13.6 X 980 dyn/cm², ρ= 0.001293 gm/cm³.

So, c = 33117 cm/s = 331.2 m/s

This value is almost identical to the experimental value. From this it can be concluded that the equation given by Laplace for the velocity of sound in gas is correct.

SPEED OF SOUND IN SOLID AND LIQUID MEDIA

Sound propagates in the form of longitudinal elastic waves through solids and liquids as well as through gases. But the speed of sound is different in different media. The speed of sound in a gaseous medium is different from the speed of sound in a solid or liquid. If E is the elastic coefficient of the material and ρ is the density, Newton’s law for the velocity of sound is,

c = √E/ρ ………(1)

The density of any solid or liquid is greater than the density of a gas. But the elastic coefficients of solids or liquids are many times higher than those of gases. As a result, the speed of sound in a solid or liquid is greater than the speed of sound in a gas. For example, the speed of sound in iron and water is about 15 times and 4.5 times the speed of sound in air, respectively.

The fact that the speed of sound in iron is greater than that in air is easily understood by a simple experiment. If one end of a long iron pipe is struck hard, the sound of the blow is heard twice at the other end. The first time is heard for propagation of sound through the iron, and the second time is heard for propagation of sound through the air inside the tube (for this test to be successful, an iron pipe of at least 100 meters long must be taken, otherwise the gap between the two sounds is almost indiscernible).

A distinction is noted between these two substances—solid and liquid—as a medium of speech. The elastic modulus of a solid that comes into the calculation is its Young’s modulus (Y).

On the other hand, for liquids as well as for gases, only one elastic coefficient is used in all cases. That is its bulk modulus (k). Hence, the form of equation (1) for solid and liquid is respectively,

c = √Y/ρ ……(2)

& c = √k/ρ …….(3)

For steel, Y = 2 X 10¹¹ N/m²; ρ = 7850 kg/m³; Hence from equation (2) we get,

c = 5048 m/s

For water, k = 2.1 X 10⁹ N/m²; ρ = 1000 kg/m³; Hence from equation (3) we get,

c = 1449 m/s

CONCLUSION

The velocity of sound changes depending on the medium it passes through, with solids having the highest speed, followed by liquids, and then gases. Its speed is also influenced by factors such as temperature, pressure, and density. Knowing these factors is essential in disciplines such as acoustics, engineering, and atmospheric research.

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