Propagation Of Sound Wave: Examples

Propagation Of Sound Wave

Edited By Vishal kumar | Updated on Jul 02, 2025 05:34 PM IST

Sound waves are mechanical oscillations moving through a medium such as air, water, or solid materials; they’re created by any object that vibrates and makes the surrounding medium vibrate too. The sound spreads from continuously moving one thing creating regions of high density and low compression behind itself, bringing about a waveform which we hear as noise.

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What Is Sound And Sound Wave?
Solved Examples Based on Sound Wave
Summary

Propagation Of Sound Wave

In this article, we will discuss the sound waves and propagation of sound waves which are important when studying oscillations, and physics courses that apply to NEET and JEE Main. Most times, understanding sound waves makes it easy to understand other things like wave propagation, frequency and also wavelength. Longitudinal waves are sound waves that transport power.

What Is Sound And Sound Wave?

Sound is defined as the energy to which the human ears are sensitive is known as sound.

Sound waves always travel through any elastic material medium with a speed that depends on the properties of the medium. As sound waves travel through the air, the molecules of air vibrate to produce changes in density and pressure along the direction of motion of the wave. If the source of the sound waves vibrates as a Sine wave, the pressure variations are also like Sine waves. Because of this, the mathematical description of sinusoidal sound waves is very similar to that of sinusoidal waves on strings.

Propagation of Sound Waves

Sound is a longitudinal wave that is created by a vibrating source such as a guitar string, the human vocal cords, or the diaphragm of a loudspeaker. As a sound wave is a mechanical wave, so, sound needs a medium having properties of inertia and elasticity. To understand the propagation of sound waves. let us take an example -

Consider a tuning fork producing sound waves. When prong B moves outward towards the right it compresses the air in front of it and due to compression, the pressure in this region rises slightly. The region where pressure is increased is called a compression pulse and it travels away from the prong with the speed of sound.

Now, after producing the compression pulse, prong B reverses its motion and moves inward. This process drags away some air from the region in front of it, which causes the pressure to dip slightly below the normal pressure. This region is a decreased pressure region which is called a rarefaction pulse. Following immediately behind the compression pulse, the rarefaction pulse also travels away from the prong with the speed of sound. If the prongs vibrate in SHM then the pressure variation in the layer close to the prong also varies simply harmonically and shows SHM hence increase in pressure above normal value can be written as -

δP=δP0sin⁡ωt

Here,

δP0 is the maximum increase in value above the normal value

Now, the equation can also be written as -

δP=δP0sin⁡[ω(t−x/v)]

where, v is the wave velocity

So, the above equation shows the variation of pressure with time.

If the change in pressure is not very small then we can write the variation of pressure in the form of

Δp=Δpmaxsin⁡[ω(t−x/v)]

Solved Examples Based on Sound Wave

Example 1: The maximum pressure variation that the human ear can tolerate is 30 N/m2. The maximum displacement for a sound wave in the air having a frequency of 103kHz is? (Use density of air =ρ=1.2kgm3 and speed of sound in air =v=343 m/s )

1) 2π3×10−2 km
2) 2×10−4πkm
3) π3×10−2 km
4) 10−43πkm

Solution:

Equation of sound wave

ΔP=ΔPmax⋅sin⁡[ω(t−xv)]
wherein
ΔP= variation in pressure at a point
ΔPmax= maximum variation in pressure
(ΔPmax )=BAK⇒A=ΔPBkv=ωkB=ρ×v2

k=ωρB⇒A=ΔPmax2πfρv=10−43πKm
(Use ρ=1.2kgm3 and v=343 m/s )

Hence, the answer is the option (4).

Example 2: The pressure wave, P=0.01sin⁡[1000t−3x]Nm−2, corresponds to the sound produced by a vibrating blade on a day when the atmospheric temperature is 0∘C.On some other day when the temperature is T. the speed of sound produced by the same blade and at the same frequency is found to be 336 ms−1. Approximate value of T (in ∘C ) is:

1) 4

2) 11

3) 12

4) 15

Solution:

Equation of sound wave

ΔP=ΔPmax⋅sin⁡[ω(t−xV)] wherein ΔP= variation in pressure at a point ΔPmax= maximum variation in pressure at 0∘CP=0.01sin⁡(1000t−3x)Nm−2V1=ωkV1=10003 at temp TV2=336 ms−1

V1V2=T1T210003336=273T⇒T=277.41k=T=4.4∘C
(Where T is in Kelvin)

Hence, the answer is option (4).

Example 3: Sound velocity is maximum in

1) H₂

2) N₂

3) He

4) O₂

Solution:

Effect of pressure on the speed of sound -

For ideal gas

Pρ=RTM= constant

wherein

With the change in pressure, the density also changes so the pressure does not affect the speed of sound.

v=γRTM⇒v∝γM

Since γM is maximum for H2, so sound velocity is maximum in H2.

Hence, the answer is the option 1.

Example 4: The ratio of densities of nitrogen and oxygen is 14:16. The temperature at which the speed of sound in nitrogen will be the same as that in oxygen at 55∘C is:

1) 35∘C
2) 48∘C
3) 65∘C
4) 14∘C

Solution:

v=γRTM⇒TNTO=MNMO (since the given velocities are the same) ⇒TN273+55=1416=78⇒TN=287 K=14∘C

Hence, the answer is the option 4.

Example 5: If the temperature of the atmosphere is increased, the following character of the sound wave is affected

1) Amplitude

2) Frequency

3) Velocity

4) Wavelength

Solution:

Effect of temperature on the speed of sound

∵Pρ=RTM∴V=γRTM
wherein
V∝T
T is in Kelvin
So velocity increases with an increase in temperature.
vαT

Hence, the answer is the option (3).

Summary

Sound waves move through air, water, or other substances by vibrating. This makes the particles in these substances move forwards and backwards with compressed and stretched regions being created along the way. Vibrations enable transmission of energy through one particle at a time thereby facilitating movement of sound waves in space and time.

Frequently Asked Questions (FAQs)

1. A medium can carry a longitudinal wave due to which the property?

If the medium has good elasticity it will have a tendency to regain its original dimension when disturbed during

2. It is true that sound waves are longitudinal while light waves are transverse.

Yes

3. When we hear a sound, we can identify its source?

The sounds of different sources are said to differ in quality. The number of overtones and their relative intensities determine the quality of any musical sound.

4. Quality depends upon?

Quality Depends upon Timbre (which is also called timber, the quality of auditory sensations produced by the tone of a sound wave)

5. What is the Doppler effect?

The Doppler effect is the change in frequency of a sound wave as perceived by an observer when the source of the sound is moving relative to the observer. It causes the pitch of an approaching sound source to seem higher and a receding source to seem lower.

6. What is meant by the term "acoustic radiation pressure"?

Acoustic radiation pressure is the small, time-averaged force exerted by a sound wave on a surface. It results from the transfer of momentum from the sound wave to the surface and can be used in applications such as acoustic levitation or ultrasonic cleaning.

7. How does sound intensity decrease with distance from the source?

Sound intensity decreases with distance from the source according to the inverse square law. This means that as the distance from the source doubles, the sound intensity decreases to one-fourth of its original value, assuming the sound spreads out equally in all directions.

8. What is meant by the term "acoustic impedance matching"?

Acoustic impedance matching refers to the process of minimizing sound reflection at the interface between two media by making their acoustic impedances as similar as possible. This is important in various applications, such as designing efficient speakers or medical ultrasound devices.

9. What is acoustic streaming?

Acoustic streaming is a steady fluid flow induced by high-intensity sound waves in a fluid medium. It results from the transfer of momentum from the sound wave to the fluid and can occur in both liquids and gases. This phenomenon has applications in mixing, heat transfer, and ultrasonic cleaning.

10. What is a sound wave?

A sound wave is a type of mechanical wave that propagates through a medium (such as air, water, or solids) by the vibration of particles. It involves the transfer of energy through the medium without the transfer of matter.

11. How does sound travel through different mediums?

Sound travels through different mediums by the vibration of particles. In solids, it propagates through the vibration of atoms in the crystal lattice. In liquids and gases, it travels through the compression and rarefaction of molecules.

12. Why can't sound travel through a vacuum?

Sound cannot travel through a vacuum because it requires a medium to propagate. In a vacuum, there are no particles to vibrate and transfer energy, so sound waves cannot form or travel.

13. What determines the speed of sound in a medium?

The speed of sound in a medium is determined by the medium's properties, primarily its density and elasticity. In general, sound travels faster in denser and more rigid materials.

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

Temperature affects the speed of sound in air by changing the kinetic energy of air molecules. As temperature increases, the molecules move faster, allowing sound waves to propagate more quickly. The speed of sound in air increases by about 0.6 m/s for every 1°C rise in temperature.

15. What is the difference between near field and far field in acoustics?

In acoustics, the near field is the region close to a sound source where the sound pressure and particle velocity are not in phase and the sound field is complex. The far field is the region farther from the source where the sound behaves more like a plane wave, with pressure and velocity in phase.

16. What is acoustic metamaterial?

Acoustic metamaterials are artificially structured materials designed to control, direct, and manipulate sound waves in ways not possible with conventional materials. They can exhibit properties such as negative refractive index or acoustic cloaking, enabling novel applications in sound control and manipulation.

17. What is the role of acoustic absorption in room acoustics?

Acoustic absorption is crucial in room acoustics for controlling reverberation and echo. Absorptive materials convert sound energy into heat through friction, reducing reflections and improving sound clarity. This is important for creating suitable acoustic environments in concert halls, recording studios, and other spaces.

18. What is the difference between longitudinal and transverse waves?

Longitudinal waves have particle vibrations parallel to the direction of wave propagation, while transverse waves have particle vibrations perpendicular to the direction of wave propagation. Sound waves are longitudinal waves.

19. What are compressions and rarefactions in a sound wave?

Compressions are regions in a longitudinal wave where particles are closer together, creating areas of higher pressure. Rarefactions are regions where particles are farther apart, creating areas of lower pressure. These alternating regions form the sound wave.

20. How does the amplitude of a sound wave relate to its loudness?

The amplitude of a sound wave is directly related to its loudness. A larger amplitude results in a louder sound, while a smaller amplitude produces a quieter sound. Amplitude is a measure of the maximum displacement of particles from their equilibrium position.

21. What is the relationship between frequency and pitch in sound waves?

Frequency and pitch are directly related. Higher frequency sound waves are perceived as having a higher pitch, while lower frequency sound waves are perceived as having a lower pitch. The frequency of a sound wave is the number of vibrations per second.

22. How do sound waves interact with obstacles?

Sound waves can interact with obstacles in several ways: reflection (bouncing off surfaces), refraction (bending when entering a new medium), diffraction (bending around obstacles), and absorption (being partially or fully absorbed by materials).

23. How do musical instruments produce different pitches?

Musical instruments produce different pitches by varying the frequency of vibration. This can be achieved through changing the length of a vibrating string or air column, altering the tension of a string, or modifying the size of a vibrating surface.

24. What is resonance in the context of sound waves?

Resonance is the phenomenon where an object or system vibrates with greater amplitude at specific frequencies, known as its natural frequencies. In the context of sound, resonance occurs when the frequency of a forced vibration matches the natural frequency of an object, resulting in increased amplitude.

25. How do humans produce speech sounds?

Humans produce speech sounds by forcing air from the lungs through the vocal cords, which vibrate to create sound waves. The shape and movement of the mouth, tongue, and lips then modify these sound waves to form different speech sounds.

26. What is the difference between infrasound and ultrasound?

Infrasound refers to sound waves with frequencies below the lower limit of human hearing (typically 20 Hz), while ultrasound refers to sound waves with frequencies above the upper limit of human hearing (typically 20 kHz). Both are inaudible to humans but can be detected by certain animals and specialized equipment.

27. How do noise-cancelling headphones work?

Noise-cancelling headphones work by using microphones to detect ambient noise and then generating sound waves that are exactly out of phase with the detected noise. When these opposing sound waves combine, they cancel each other out through destructive interference, reducing the perceived noise.

28. What is acoustic impedance?

Acoustic impedance is a measure of how much a medium resists the flow of sound energy. It is defined as the product of the medium's density and the speed of sound in that medium. Acoustic impedance affects how sound waves are transmitted and reflected at the boundary between different media.

29. How does the shape of a room affect sound propagation?

The shape of a room affects sound propagation through reflection, absorption, and diffraction. Curved surfaces can focus or disperse sound waves, while flat surfaces can create standing waves. The room's dimensions can also lead to resonance at specific frequencies, influencing the overall acoustics.

30. What is meant by the term "sound intensity"?

Sound intensity is the amount of sound energy passing through a unit area perpendicular to the direction of sound propagation per unit time. It is measured in watts per square meter (W/m²) and is related to the amplitude of the sound wave and the properties of the medium.

31. What is meant by the term "acoustic shadow"?

An acoustic shadow is an area where sound waves are blocked or reduced in intensity due to an obstacle or atmospheric conditions. This can result in areas of reduced sound intensity, even when close to a sound source.

32. How do shock waves differ from regular sound waves?

Shock waves are a type of high-amplitude, high-energy disturbance that propagates faster than the speed of sound in the medium. Unlike regular sound waves, shock waves involve a nearly instantaneous change in pressure, temperature, and density, and can cause non-linear effects in the medium.

33. What is sound attenuation?

Sound attenuation is the gradual loss of sound energy as it propagates through a medium. This can occur due to absorption by the medium, scattering by inhomogeneities, or geometric spreading of the wavefront. Attenuation results in a decrease in sound intensity over distance.

34. How does humidity affect sound propagation in air?

Humidity affects sound propagation in air by changing the air's density and molecular composition. Higher humidity generally increases the speed of sound slightly and can also affect sound attenuation, particularly at higher frequencies.

35. What is acoustic refraction?

Acoustic refraction is the bending of sound waves as they pass from one medium to another with a different speed of sound. This can occur due to changes in temperature, density, or composition of the medium, and can affect the direction of sound propagation.

36. How do animals like bats and dolphins use sound for echolocation?

Bats and dolphins use echolocation by emitting high-frequency sound waves and listening to the echoes. They analyze the time delay and characteristics of the returning echoes to determine the location, size, and shape of objects in their environment, allowing them to navigate and hunt effectively.

37. How does the speed of sound in water compare to its speed in air?

The speed of sound in water is approximately 1,500 meters per second, which is about 4.3 times faster than its speed in air (about 343 meters per second at room temperature). This difference is due to water's higher density and elasticity compared to air.

38. What is acoustic levitation?

Acoustic levitation is a method of suspending matter in air using sound waves. It works by creating a standing wave pattern with areas of high and low pressure. Small objects can be trapped at the nodes of these standing waves, effectively levitating them against gravity.

39. How do sonic booms form?

Sonic booms form when an object travels faster than the speed of sound in a medium. The object creates a shock wave, which is a cone-shaped region of compressed air. When this shock wave passes an observer, it is heard as a loud "boom" sound.

40. How does sound propagation differ in solids compared to fluids?

In solids, sound can propagate as both longitudinal and transverse waves due to the strong interatomic forces. In fluids (liquids and gases), sound primarily propagates as longitudinal waves because fluids cannot support shear stresses necessary for transverse waves.

41. How does the concept of wavelength apply to sound waves?

The wavelength of a sound wave is the distance between two consecutive compressions or rarefactions. It is inversely related to the frequency of the sound wave. Lower frequency sounds have longer wavelengths, while higher frequency sounds have shorter wavelengths.

42. How do phase differences affect sound wave interference?

Phase differences determine how sound waves interfere with each other. When two waves are in phase, they reinforce each other (constructive interference), resulting in a louder sound. When they are out of phase, they cancel each other out (destructive interference), potentially resulting in silence.

43. What is the role of harmonics in sound production?

Harmonics are integer multiples of a fundamental frequency that contribute to the overall sound quality or timbre of a note. They are responsible for the unique sound characteristics of different instruments or voices, even when playing the same pitch.

44. How does sound behave at the interface between two different media?

At the interface between two media, part of the sound wave is reflected and part is transmitted. The amount of reflection and transmission depends on the acoustic impedance mismatch between the media. A larger mismatch results in more reflection and less transmission.

45. What is acoustic holography?

Acoustic holography is a technique for visualizing sound fields by recording the amplitude and phase of sound waves at different points in space. This information can be used to reconstruct the entire sound field, allowing for detailed analysis of sound sources and propagation patterns.

46. How do standing waves form in enclosed spaces?

Standing waves form in enclosed spaces when incident and reflected waves interfere. If the wavelength of the sound matches the dimensions of the space, resonance occurs, creating a pattern of nodes (points of minimum amplitude) and antinodes (points of maximum amplitude) that appear stationary.

47. What is the relationship between sound pressure level and intensity?

Sound pressure level (SPL) is a logarithmic measure of sound pressure relative to a reference value, while intensity is the amount of sound energy per unit area. SPL is proportional to the logarithm of intensity, with a 10 dB increase in SPL corresponding to a 10-fold increase in intensity.

48. How does sound diffraction occur around obstacles?

Sound diffraction occurs when sound waves encounter an obstacle or opening. The waves bend around the edges of the obstacle or spread out after passing through an opening. The amount of diffraction depends on the wavelength of the sound relative to the size of the obstacle or opening.

49. What is meant by the term "acoustic signature"?

An acoustic signature is the unique pattern of sound produced by an object or event. It can be used to identify and distinguish different sources, such as different types of vehicles, machinery, or even individual musical instruments.

50. How does the concept of group velocity apply to sound waves?

Group velocity is the velocity at which the overall shape of a wave's amplitudes propagates through space. For sound waves in non-dispersive media (where speed is independent of frequency), the group velocity is equal to the phase velocity. However, in dispersive media, these velocities can differ.

51. How do acoustic mirrors work?

Acoustic mirrors are curved surfaces designed to reflect and focus sound waves. They work on the principle that sound waves reflect off surfaces at the same angle they strike them. By carefully shaping the mirror, sound can be concentrated at a focal point or redirected in a specific direction.

52. How does sound propagation in the ocean differ from that in air?

Sound propagation in the ocean is more complex than in air due to factors such as pressure changes with depth, temperature gradients, and salinity variations. These create sound channels that can guide sound waves over long distances. Additionally, the higher density of water allows for more efficient sound transmission.

53. What is meant by the term "acoustic cloaking"?

Acoustic cloaking refers to techniques that make objects "invisible" to sound waves. This is achieved by designing materials or structures that bend sound waves around an object without scattering, making it appear as if the sound passed through empty space. It has potential applications in stealth technology and noise control.

54. How do nonlinear effects manifest in high-intensity sound waves?

In high-intensity sound waves, nonlinear effects can occur due to the medium's response to large amplitude oscillations. These effects include waveform distortion, harmonic generation, and shock formation. Nonlinear acoustics is important in applications such as medical ultrasound and acoustic levitation.