Speed of Sound Propagation - Definition, Formula, Characteristics, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:36 PM IST

Every second, we are bombarded with a variety of sounds. It could come from the instruments, thunder, or a long number of other things. But what exactly is sound? What happens when it happens? How does the sound get made? What is the process of sound propagation? Let us give you answers to all of these questions. We supply students with sound propagation notes in order for them to fully comprehend the phenomenon and the physics behind it. They will also comprehend how sound travels through various mediums and the subsequent procedure.

This Story also Contains

What is Sound?
Formula of speed of sound-
Characteristics of sound-
What is the speed of sound?
Speed of sound in different media-

Speed of Sound Propagation - Definition, Formula, Characteristics, FAQs

What is Sound?

Sound, like heat, electricity, and other forms of energy, is nothing more than a type of energy. Consider the sound of a bell as an example of a sound source. A sound is produced whenever we strike a bell. The vibration that follows the sound causes the object's body to move back and forth.

Sound is a vibration that travels through solid, liquid, and gas mediums as an acoustic wave, with the medium contracting and expanding alternately.

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Formula of speed of sound-

The following is the formula for the speed with regard to gases:

$\nu=\sqrt{\frac{\gamma P}{\rho}}$

The coefficient of adiabatic expansion is ?
The coefficient of adiabatic expansion is ?
The pressure of the gas is denoted by the letter P.
? is the density of the medium through which sound travels.

Characteristics of sound-

Sound is represented graphically as a series of continuous peaks and valleys. The wavelength of a wave is the distance spanned between two continuous peaks or troughs. The number of cycles covered per unit of time is the frequency of sound. Hertz is the unit of measurement.

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NEET Highest Scoring Chapters & Topics

This ebook serves as a valuable study guide for NEET exams, specifically designed to assist students in light of recent changes and the removal of certain topics from the NEET exam.

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What is the speed of sound?

The dynamic propagation of sound waves determines the speed of sound in air. This is determined by the properties of the medium in which the propagation occurs. In an elastic medium, the term "velocity of sound in the air" is used to describe the speed of sound in airwaves.

FACTORS AFFECTING SPEED OF SOUNDS-

The following are the primary factors that influence the sound's speed:

The Density of the Medium: Sound travels through a medium. The density of the medium is one of the parameters that influence sound speed. The faster sound goes through the medium, the higher the density. The smaller the density, on the other side, the slower the sound propagation speed. This means that the velocity of sound changes directly with the density of the medium in different media.

The Medium's Temperature: The higher the temperature, the faster the sound travels through the medium.

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Speed of sound in different media-

1. Speed of sound in solid-

Sound travels through solids by colliding with different molecules and particles. Solids have a higher density than other media, resulting in a fast sound speed. The speed of sound in solids is around 6000m/s.

2. Speed of sound in liquid-

Liquids have a lower density than solids and a higher density than gases. As a result, the speed of sound in liquids lies somewhere between that of solids and gases.

3. Speed of sound in gases-

In gases, the speed of sound is independent of the medium. This is due to the consistency of gas density, regardless of its kind.

4. Speed of sound in vacuum-

Because sound does not travel in a vacuum, its speed is zero. In a vacuum, there are no particles, therefore this happens. Sound waves do not travel through space in a vacuum.

5. Speed of sound in water-

Sound travels faster in water than it does in air. Or, to put it another way, sound travels faster in water than it does in air. In water, sound travels at a speed of 1480 meters per second. It's also worth noting that the speed of distilled water varies between 1450 and 1498 meters per second, whereas the speed of saltwater varies between 1450 to 1570 meters per second.

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NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. What feature is utilized to tell the difference between a sharp and a dull sound?

Pitch is the property that allows you to tell the difference between a sharp and a dull sound. The pitch of a sound wave is determined by its frequency. The pitch rises in proportion to the frequency.

2. Set the sound's amplitude.

The quantity of energy travelling through the unit area at that location is defined as the intensity of sound. The square of the distance between the point and the source causes it to be inversely proportional. It's also proportional to the square of the vibration and frequency, as well as the medium's density.

3. What do the various loudness units mean?

Bel, decibel and phon are the three different units of loudness.

4. Give an example of a medium where sound travels at a fast rate.

Steel.

5. Name the variables that influence the sound speed of a gas.

The density and elasticity of a gas influence the speed of air sound in it.

6. What factors influence sound speed?

The speed varies based on atmospheric conditions, with the temperature being the most critical element. Air pressure has no effect on the speed of sound, and neither does the humidity. In a perfect gas approximation, air pressure has no influence.

7. Why do sounds travel faster in hot air than in cold air?

Heat causes air molecules to travel more quickly, making them better suited to carrying a pressure wave than slower-moving molecules. As a result, heat causes the sound to travel faster.

8. Why does the pitch of a siren change as it passes by?

The change in pitch of a passing siren is due to the Doppler effect. As the source of sound approaches, the perceived frequency (pitch) increases because sound waves are compressed. As it moves away, the perceived frequency decreases because the waves are stretched out.

9. How does atmospheric pressure affect the speed of sound?

Atmospheric pressure itself does not directly affect the speed of sound. However, changes in pressure often coincide with changes in temperature or density, which do affect sound speed. In general, the speed of sound is independent of pressure for an ideal gas.

10. How does the speed of sound in air change with humidity at constant temperature?

As humidity increases at constant temperature, the speed of sound in air slightly increases. This is because water vapor molecules are less massive than nitrogen and oxygen molecules, reducing the average molecular mass of the air and allowing sound waves to propagate faster.

11. How does the speed of sound relate to the concept of refraction?

Refraction of sound occurs when sound waves pass from one medium to another with a different speed of sound. The change in speed causes the waves to bend, similar to light refraction. This principle is used in various applications, such as underwater acoustics and seismic exploration.

12. What is the relationship between the speed of sound and the compressibility of a medium?

The speed of sound is inversely proportional to the square root of the compressibility of the medium. Materials with lower compressibility (higher stiffness) tend to have higher speeds of sound. This is why sound typically travels faster in solids than in liquids or gases.

13. What is the formula for the speed of sound in a gas?

The formula for the speed of sound in an ideal gas is v = √(γRT/M), where v is the speed of sound, γ is the ratio of specific heats, R is the gas constant, T is the absolute temperature, and M is the molar mass of the gas.

14. What is the relationship between wavelength, frequency, and speed of sound?

The relationship between wavelength (λ), frequency (f), and speed of sound (v) is given by the equation: v = λf. This means that for a constant speed of sound, as frequency increases, wavelength decreases, and vice versa.

15. What is the adiabatic index, and how does it relate to the speed of sound?

The adiabatic index, also known as the ratio of specific heats (γ), is a factor in the speed of sound formula for gases. It represents the ratio of heat capacity at constant pressure to heat capacity at constant volume. A higher adiabatic index results in a higher speed of sound in a gas.

16. What is the relationship between the speed of sound and the bulk modulus of a material?

The speed of sound in a material is directly related to its bulk modulus, which measures the material's resistance to uniform compression. The higher the bulk modulus, the faster sound travels through the material. This relationship is expressed in the formula: v = √(B/ρ), where v is the speed of sound, B is the bulk modulus, and ρ is the density.

17. What is the relationship between the speed of sound and the density of a medium?

In general, the speed of sound is inversely proportional to the square root of the density of the medium. This means that as the density of a medium increases, the speed of sound typically decreases, assuming other factors remain constant.

18. How does the speed of sound compare in different mediums?

The speed of sound varies in different mediums. Generally, it travels fastest in solids, slower in liquids, and slowest in gases. This is because the speed of sound depends on the density and elasticity of the medium.

19. Why does sound travel faster in solids than in gases?

Sound travels faster in solids because the particles in solids are closer together and more tightly bound. This allows for quicker transfer of vibrations between particles, resulting in faster sound propagation compared to gases where particles are far apart.

20. How does temperature affect the speed of sound in air?

Temperature directly affects the speed of sound in air. As temperature increases, the speed of sound increases. This is because higher temperatures cause air molecules to move faster, allowing sound waves to propagate more quickly.

21. Does humidity affect the speed of sound in air?

Yes, humidity affects the speed of sound in air. In humid air, sound travels slightly faster than in dry air at the same temperature. This is because water vapor molecules are lighter than nitrogen and oxygen molecules, reducing the average molecular weight of the air.

22. What is the Mach number, and how is it related to the speed of sound?

The Mach number is a dimensionless quantity representing the ratio of an object's speed to the speed of sound in the surrounding medium. An object traveling at Mach 1 is moving at the speed of sound, while Mach numbers greater than 1 indicate supersonic speeds.

23. How does the speed of sound relate to shock waves?

Shock waves form when an object moves faster than the speed of sound in a medium. The shock wave is a thin region of compressed medium where properties like pressure, temperature, and density change abruptly. The speed of sound plays a crucial role in determining when and how shock waves form.

24. What is acoustic impedance, and how is it related to the speed of sound?

Acoustic impedance is the product of the density of a medium and the speed of sound in that medium. It characterizes how much sound pressure is generated by a given air vibration in a particular medium. Materials with different acoustic impedances cause reflection and transmission of sound waves at their interfaces.

25. What is the relationship between the speed of sound and the temperature of absolute zero?

As temperature approaches absolute zero, the speed of sound in most materials approaches zero. This is because molecular motion nearly ceases at absolute zero, making it extremely difficult for sound waves (which are mechanical waves) to propagate through the medium.

26. What is the Newton-Laplace equation, and how does it relate to the speed of sound?

The Newton-Laplace equation describes the speed of sound in an elastic medium: v = √(K/ρ), where v is the speed of sound, K is the bulk modulus of elasticity, and ρ is the density of the medium. This equation is fundamental in understanding how material properties affect sound propagation.

27. How does the speed of sound change in the presence of turbulence?

Turbulence in a fluid can affect the propagation of sound waves. It can cause scattering and refraction of sound waves, leading to changes in the effective speed and direction of sound propagation. In highly turbulent flows, sound can be attenuated or dispersed more rapidly than in laminar flows.

28. What is the speed of sound?

The speed of sound is the rate at which sound waves travel through a medium. It represents how quickly sound energy propagates from one point to another in a substance, such as air, water, or solid materials.

29. Why do we hear thunder after seeing lightning?

We hear thunder after seeing lightning because light travels much faster than sound. Light from the lightning reaches our eyes almost instantaneously, while the sound waves (thunder) travel at the speed of sound, which is much slower, causing a delay between seeing and hearing.

30. How can we use the speed of sound to estimate the distance of a thunderstorm?

To estimate the distance of a thunderstorm, count the number of seconds between seeing the lightning flash and hearing the thunder, then divide by 5. This gives you the approximate distance in miles (or divide by 3 for kilometers). This method works because sound travels about 1 mile in 5 seconds.

31. What is a sonic boom?

A sonic boom is a loud, explosive noise caused by the shock waves created when an object travels through the air faster than the speed of sound. It occurs when the sound waves created by the object pile up and combine into a single shock wave.

32. How does the speed of sound change with altitude in the atmosphere?

The speed of sound generally decreases with increasing altitude in the lower atmosphere (troposphere) due to decreasing temperature. However, in the stratosphere, the speed of sound may increase due to rising temperatures caused by ozone absorption of UV radiation.

33. How does the speed of sound in water compare to that in air?

The speed of sound in water is about 4.3 times faster than in air at room temperature. This is due to water's higher density and lower compressibility compared to air, allowing sound waves to propagate more quickly.

34. What is the speed of sound at sea level and 20°C (68°F)?

At sea level and 20°C (68°F), the speed of sound in air is approximately 343 meters per second (m/s) or 1,235 kilometers per hour (km/h). This value is often used as a reference point in calculations involving sound propagation.

35. How does the speed of sound in metals compare to that in air?

The speed of sound in metals is much higher than in air. For example, sound travels about 15 times faster in steel than in air. This is due to the higher density and stronger interatomic bonds in metals, allowing for more efficient energy transfer between particles.

36. How does the speed of sound change during a phase transition, such as from liquid to gas?

During a phase transition, the speed of sound can change dramatically. For example, when water changes from liquid to gas (steam), the speed of sound decreases significantly due to the large decrease in density and change in molecular structure.

37. What is the significance of the critical temperature in relation to the speed of sound?

The critical temperature is the temperature above which a gas cannot be liquefied by pressure alone. Near the critical temperature, the speed of sound in a substance can change dramatically due to significant changes in the material's compressibility and density.

38. How does the speed of sound in a gas change if the gas molecules have more degrees of freedom?

If gas molecules have more degrees of freedom (ways to store energy), the speed of sound in that gas decreases. This is because more energy goes into internal motions of the molecules rather than translational motion, reducing the effective temperature and thus the speed of sound.

39. How does the speed of sound change in the ocean at different depths?

The speed of sound in the ocean varies with depth due to changes in temperature, pressure, and salinity. It generally decreases with depth in the upper layers due to decreasing temperature, then increases in deeper layers due to increasing pressure, creating a "sound channel" where sound can travel long distances.

40. What is the difference between group velocity and phase velocity in sound waves?

Group velocity is the speed at which the overall shape of a wave's amplitudes travels, while phase velocity is the speed at which the phase of any one frequency component of the wave travels. In non-dispersive mediums, these velocities are the same for sound waves, but they can differ in dispersive mediums.

41. How does the speed of sound change in a gas mixture compared to its pure components?

The speed of sound in a gas mixture is generally different from that in its pure components. It depends on the average molecular weight and the ratio of specific heats of the mixture. The speed can be calculated using mixture rules that consider the proportions and properties of each component.

42. What is the role of mean free path in determining the speed of sound in gases?

The mean free path, which is the average distance a molecule travels between collisions, affects the speed of sound in gases. A shorter mean free path generally results in a higher speed of sound because energy is transferred more quickly between molecules through more frequent collisions.

43. How does the speed of sound change during a chemical reaction in gases?

The speed of sound can change during a chemical reaction in gases due to changes in temperature, molecular composition, and the ratio of specific heats. For example, in combustion reactions, the speed of sound often increases due to the higher temperature and changes in gas composition.

44. How does the speed of sound in a solid change with crystal structure?

The speed of sound in a solid can vary with crystal structure due to differences in interatomic forces and arrangements. Anisotropic crystals may have different sound speeds in different directions, while isotropic materials have the same speed in all directions. The elastic constants of the crystal determine these variations.

45. How does the presence of suspended particles in a fluid affect the speed of sound?

Suspended particles in a fluid can affect the speed of sound by changing the fluid's effective density and compressibility. Depending on the size, concentration, and properties of the particles, they can either increase or decrease the speed of sound compared to the pure fluid.

46. What is the significance of the Wood's equation in understanding the speed of sound in porous materials?

Wood's equation relates the speed of sound in a porous material to its porosity, density, and the properties of both the solid frame and the fluid in the pores. It's particularly useful in geophysics and materials science for understanding sound propagation in complex, multi-phase media like rocks or foams.

47. How does the speed of sound change in supercritical fluids?

In supercritical fluids, which exist above the critical point where distinct liquid and gas phases do not exist, the speed of sound can exhibit unusual behavior. It often goes through a minimum near the critical point due to large fluctuations in density and compressibility in this region.

48. What is the relationship between the speed of sound and the Knudsen number in rarefied gases?

The Knudsen number, which is the ratio of the mean free path to a characteristic length scale, affects sound propagation in rarefied gases. As the Knudsen number increases (gas becomes more rarefied), the continuum assumption breaks down, and the classical speed of sound formula becomes less accurate.

49. How does the speed of sound change in plasma compared to neutral gases?

The speed of sound in plasma is generally higher than in neutral gases due to the presence of free electrons and ions. In plasma, there are additional modes of wave propagation, such as ion-acoustic waves, which can have different propagation speeds compared to neutral sound waves.

50. What is the effect of magnetic fields on the speed of sound in conducting fluids or plasmas?

Magnetic fields can significantly affect the speed of sound in conducting fluids or plasmas. They introduce additional restoring forces, leading to magnetoacoustic waves. The speed of these waves depends on the strength and orientation of the magnetic field relative to the direction of wave propagation.

51. What is the relationship between the speed of sound and the equation of state for a material?

The speed of sound is directly related to the equation of state of a material, which describes how properties like pressure, volume, and temperature are interrelated. The speed of sound can be derived from the equation of state by considering how pressure changes with density at constant entropy.

52. How does the speed of sound change in non-Newtonian fluids?

In non-Newtonian fluids, where viscosity changes with applied stress or strain rate, the speed of sound can be more complex than in Newtonian fluids. It may depend on the frequency of the sound waves and the current state of the fluid, leading to dispersive behavior where different frequencies travel at different speeds.

53. What is the significance of the Grüneisen parameter in determining the speed of sound in solids?

The Grüneisen parameter relates the change in pressure to the change in internal energy for a given change in volume. It plays a crucial role in determining how the speed of sound in solids changes with temperature and pressure, especially at high pressures and temperatures encountered in geophysics and materials science.

54. How does the speed of sound change in the presence of chemical reactions or phase transitions?

During chemical reactions or phase transitions, the speed of sound can change abruptly due to changes in density, compressibility, and molecular structure. These changes can lead to interesting acoustic phenomena, such as acoustic emissions during phase transitions or chemical reactions in materials.

55. What is the relationship between the speed of sound and the bulk viscosity of a fluid?

The bulk viscosity of a fluid, which relates to its resistance to rapid compression or expansion, can affect the speed of sound, especially at high frequencies. Fluids with higher bulk viscosity tend to have slightly lower speeds of sound due to increased dissipation of acoustic energy.

56. How does the speed of sound in nanomaterials differ from bulk materials?

The speed of sound in nanomaterials can differ significantly from bulk materials due to surface effects, confinement, and changes in elastic properties at the nanoscale. In some cases, nanomaterials may exhibit higher speeds of sound due to increased stiffness, while in others, the speed may decrease due to softening of elastic constants.

57. What is the significance of the Landau-Placzek ratio in understanding sound propagation in fluids?

The Landau-Placzek ratio is the ratio of the intensity of the central Rayleigh peak to the Brillouin peaks in light scattering experiments. It provides information about the relative contributions of thermal and acoustic modes to density fluctuations in fluids, which in turn relates to sound propagation characteristics and thermodynamic properties of the fluid.