Mechanical waves are classified as longitudinal waves and transverse waves. Some examples of longitudinal waves are sound waves, seismic P-waves, and ultrasound waves. Transverse waves examples include electromagnetic waves and ocean waves. In this article, we will learn what is a longitudinal wave and its characteristics.
- What is Longitudinal Wave?
- Longitudinal Wave Formula
- Sound Waves
- Pressure Waves
- Characteristics of Longitudinal Waves
- Difference Between Longitudinal And Transverse Wave
- Frequently Asked Questions – FAQs
What Is Longitudinal Wave?
Longitudinal waves are waves where the displacement of the medium is in the same direction as the direction of the travelling wave.
The distance between the centres of two consecutive regions of compression or the rarefaction is defined by wavelength,λ. When the compression and rarefaction regions of two waves coincide with each other, it is known as constructive interference and if the regions of compression and rarefaction do not coincide, it is known as destructive interference.
Compression in a longitudinal wave is a region where the particles are the closest together while rarefaction in a longitudinal wave is a region where the particles are spread out.
Similar Reading: Transverse Waves
Longitudinal Wave Formula
\(\begin{array}{l}y(x,t)=y_{0}cos[\omega (t-\frac{x}{c})]\end{array} \)
Where,
- y is the displacement of the point on the travelling sound wave
- x is the distance the point travelled from the wave’s source
- t is the time elapsed
- y0is theamplitude of the oscillations
- c is the speed of the wave
- ω is the angular frequency of the wave
Quantity x/c = time ( wave takes to travel the distance x).
The frequency (f) of the wave is given by the formula:
f=ω2π
Hope you have understood what is a longitudinal wave along with its formula. Let us now learn about sound waves and pressure waves in detail.
Sound Waves
A sound wave is an example of a longitudinal wave and is produced by the vibrating motion of the particles that travel through a conductive medium. An example of sound waves in a longitudinal direction is the tuning fork.
In Sound waves, the amplitude of the wave is the difference between the maximum pressure caused by the wave and the pressure of the undisturbed air. The propagation speed of sound depends upon the type, composition of the medium, and temperature through which it propagates.
See the video below to understand the motion of longitudinal waves and transverse waves.
Pressure Waves
The pressure wave is defined as the propagation of disturbance in a medium as the pressure varies.
A harmonic pressure wave oscillation will be,
y(x,t)=y0cos(kx-ωt+φ)
Where,
- y0is the amplitude of displacement
- k is the wavenumber
- x is the distance along the axis of propagation
- ω is the angular frequency
- t is the time
- φ is the phase difference
Characteristics of Longitudinal Waves
Compression
In a longitudinal wave, compression is a region in which the particles of the wave are closest to each other.
Rarefaction
Rarefaction in a longitudinal wave takes place when the particles are farthest apart from each other.
Wavelength
The distance between two consecutive points in a longitudinal wave is known as wavelength. These consecutive points can be between two compressions or between two rarefactions.
Amplitude
Amplitude is the maximum displacement of the particle from its rest point. In a longitudinal wave, the distance from the equilibrium position in the medium to compression or rarefaction is the amplitude.
Period and Frequency
The time taken by the wave to move one wavelength is known as the period.
The frequency of the longitudinal wave is the number of wavelengths per second.
Difference Between Longitudinal And Transverse Wave
| Longitudinal Wave | Transverse Wave |
| A wave that moves in the direction of its propagation | A wave that moves in the direction perpendicular to its propagation |
| A sound wave is an example of a longitudinal wave | Water waves are an example of a transverse wave |
| It is made of refractions and compressions | It is made of troughs and crests |
| This wave can be produced in any medium such as gas, liquid or solid | This wave can be produced in solid and liquid’s surface |
Read More: Difference Between Longitudinal Waves and Transverse Waves
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Frequently Asked Questions – FAQs
Q1
The longitudinal wave formula is given by the equation _____.
y(x,t)=yocos[w(t-x/c)]
Q2
List the characteristics of sound?
The characteristics of the sound are as follows:
- Loudness
- Pitch
- Quality
Q3
What happens when a pebble is dropped into a pond with still water?
When a pebble is dropped into a pond with still water, there is the formation of ripples on the surface of the water. These ripples are in the circular form and spread out forming alternate crests. This disturbance is caused due to the kinetic energy of the particles that oscillate and the energy gets transferred to the next layer forming ripples.
Q4
State true or false: Mechanical waves are also known as elastic waves.
The given statement is true. Mechanical waves are also known as elastic waves because they depend on the elastic property of the waves.
Q5
Name the condition in which sound waves can travel through the gas.
For a sound wave to travel through the gas, the required condition is an adiabatic condition. This is because when the sound waves travel they produce compressions and rarefactions which results in the generation of heat. Therefore, for the waves to travel through the gas, the temperature must be constant. Hence, the ideal condition would be an adiabatic condition.
Q6
What is a mechanical wave?
A mechanical wave is a type of wave that is generated by the oscillation matter, which transmits energy through the propagating medium.
Q7
What are the two types of mechanical waves?
Longitudinal waves and transverse waves are the two types of mechanical waves.
Q8
What is meant by a longitudinal wave?
A longitudinal wave is a type of wave in which the medium’s vibration is parallel to the direction of the wave, and the medium’s displacement is in the same direction as that of the wave movement.
Q9
What are the main characteristics of a longitudinal wave?
Compression, rarefaction, wavelength, amplitude, period and frequency are the main characteristics of a longitudinal wave.
Q10
What are the familiar examples of longitudinal waves?
Tsunami waves, seismic-P waves, sound waves, and vibration in spring are some of the familiar examples of longitudinal waves.
Q11
What are the main differences between a Longitudinal wave and a transverse wave?
A longitudinal wave is a type of wave that travels in the direction of the medium, but a transverse wave is another type of wave that travels in the direction of the medium. Longitudinal waves are made of compressions and rarefactions, while transverse waves are made of crests and troughs.
Q12
What is constructive interference?
When the compression and rarefaction regions of two waves coincide with each other, it is known as constructive interference and if the regions of compression and rarefaction do not coincide, it is known as destructive interference.
Q13
What is a transverse wave?
A transverse wave is a moving wave whose oscillations are perpendicular to the direction of the wave. A simple demonstration of the wave can be created on a horizontal length of the string by securing one end of the string and moving the other up and down.
Q14
What are longitudinal waves?
Longitudinal waves are the waves where the displacement of the medium is in the same direction as the direction of the travel of the wave.
Q15
Define amplitude.
Amplitude is the maximum displacement of the particle from its rest point. In a longitudinal wave, the distance from the equilibrium position in the medium to compression or rarefaction is the amplitude.
Q16
What is wavelength?
The distance between two consecutive points in a longitudinal wave is known as wavelength. These consecutive points can be between two compressions or between two rarefactions.
