How Transverse Waves Travel: Why And Detailed Explanations

January 21, 2024March 22, 2022 by Raghavi Acharya

In this post, we will know the explanation of how transverse waves travel and the medium of their propagations.

Usually, transverse waves come under the category of mechanical waves; the particles or atoms in transverse waves move perpendicularly, considering the wave’s direction. The vibrations produced in the movement will help us know the path at the microscopic level.

Now to study and understand the detailed explanations of how transverse waves travel.

What can transverse waves travel through?

Transverse waves are a type of mechanical wave that surely does not need any medium to travel.

Under the category of transverse waves, we can consider electromagnetic waves as the best example. These electromagnetic waves can pass through a vacuum because the vacuum is a specific region where can find no matter, which also infers a medium’s absence. These waves are generated from a primary source and propagate through the regions’ up and down movement.

Apart from the vacuum, they can only pass through solid matter. It’s time to know a detailed explanation of how they pass through the void.

how transverse waves travel — **Image Credit: Pixabay free images**

Can transverse waves travel through a vacuum?

Transverse waves such as light and electromagnetic waves can pass through the vacuum region.

The primary source of light and electromagnetic radiation is the sun, and the light reaches us in the form of visible light that travels through the space or vacuum region; they can travel through the vacuum due to the nature of the movement of particles, that involves the displacement of particles in a perpendicular path. This movement of particles in the form of a wave is considered transverse waves that pass through the vacuum.

One more important thing to be noted is that vacuum never consists of any medium, and transverse waves are known to travel without the need for a medium. Both these factors help in the displacement of transverse waves through the vacuum.

To study in what process transverse waves travel through a vacuum.

How can transverse waves travel through a vacuum?

In general, transverse waves do not require a particular medium to propagate.

The movement of particles in transverse waves; is to be considered to analyze how they pass through a vacuum region where there is no single entity of matter or medium. In general, we studied that transverse waves move in a perpendicular path to the movement of particles in the direction of wave movement. This movement helps the particles displace in a region fully covered by space.

These waves also consist of waves with higher wavelengths, such as light waves, that travel through space or vacuum without any problem.

Now to understand how these transverse waves are created.

How transverse waves travel and created?

All the transverse waves are created through some vibrations. These vibrations are usually generated via the movement of particles upward and downward.

Transverse waves, as we know, already move in a direction that will be 90 degrees to the general wave movement of the particles. After creating due to the vibration, they move in the matter, and if they are solid medium, the wave motion will proceed smoothly. It generally depends on the medium of transmission.

Now to know the source of where these transverse waves come from.

Where do transverse waves come from?

Inelastic solids, we commonly observe these transverse waves.

The unique notion of elastic solids contains shear stress; the movement of the particles during this stress is perpendicular to the wave displacement. This vertical movement of atoms will constitute the transverse waves created from the source. The oscillations generated contribute in the case of these solid atoms’ motion.

To study the significant and fundamental difference between longitudinal and transverse waves.

Difference Between Longitudinal and Transverse Waves

The significant difference between both the longitudinal and transverse can be described in simple words as follows,

Parameters	Longitudinal	Transverse
Direction	The direction of the atoms in the longitudinal wave is towards the direction of wave movement.	The direction of the atoms in the transverse wave is always in the perpendicular direction of wave movement.
Components of the wave	Usually, it consists of crests and troughs.	All the transverse waves consist of rare fractions and compressions.
Medium of Propagation	Through all the medium of matter	Solids
Displacement	Parallel movement of energy.	Perpendicular movement of energy.
Examples	A typical example is sound waves.	A typical example is light waves.

Now let us study the detailed explanations of examples of transverse waves.

Examples Of Transverse Waves

The typical examples that we found in the medium in which the particles undergo up and down motion come under transverse waves. Some fundamental examples of transverse waves are as follows,

The ripples produced on the layer of any water surface
The secondary waves generated during an earthquake
All the Electromagnetic waves
The waves caused on a string due to vibration
Human wave formation
The water waves
Rope

The ripples produced on the layer of any water surface

When you throw any object on the water layer, it will create random movement on that surface, known as ripples. It is generated due to the spontaneous activities due to that object, and the vibrations move up and down, producing transverse waves. It can be considered to be a typical transverse wave example.

The secondary waves generated during an earthquake

Transverse waves are generated even during the earthquake; these waves are produced as a secondary element. The rapid movement of the particles inside the earth’s core generates waves that displace up and down and moves in a 90-degree direction. It is an excellent example in which we can notice the movement of particles.

All the Electromagnetic waves

Electromagnetic waves are one of the best examples of transverse waves. The waves such as radio waves, microwaves, IR waves, UV waves, and other forms come under electromagnetic waves. The motion of particles in these waves is seen as traveling in the path perpendicular to the whole wave displacement. We can know the movement since they pass through the vacuum region.

The waves are generated on a string due to vibration

When you pull a string, it starts to vibrate; due to this vibration, the particle movement starts that is seen in the form of a wave. Even here, the motion of the atoms will be perpendicular to the path of wave movement. So, it can be an example of a transverse wave.

Human wave formation

The human wave formation seen in the stadium during specific matches can be a good visualized example of transverse waves.

The water waves

Even in the waves created in the water due to its displacement, it can be considered an example of transverse waves. The big waves that rise above the water layer are seen moving in a normal direction to the total wave motion. At this stage, the movement of particles comes under transverse waves.

Rope

When you play with a rope and swing it, a wave is created; it is nothing but transverse waves. Even in its displacement, we can see the particles passing in a perpendicular path. That rope’s up and down motion will be considered to be a prominent example of transverse waves.

To study the detailed facts of explanations on the speed of transverse waves.

Factors affecting Speed of a Transverse Wave

We know that all the waves consist of crests and troughs that help displace particles present in the object. Crests are considered the topmost point, while troughs are the bottom points observed in any wave.

All the below terms play a significant factor in affecting the speed of transverse waves.

Amplitude – The speed of transverse waves does not contribute much to changing the speed of transverse waves.

Wavelength – will observe the longer wavelengths in transverse waves.

Medium – It displaces easily in solid matter.

Frequency – Frequency and time of the displacement of transverse waves can estimate its speed.

The above are some of the essential terms that are important to know while estimating transverse waves’ speed.

Frequently Asked Questions | FAQs

Explain the definition of Transverse Waves?

Transverse waves come under the category of mechanical waves.

To quickly define a transverse wave, we must first observe how a transverse wave displaces. In any transverse waves, the movement of each particle is in the perpendicular direction in consideration of the wave movement. All the particles in transverse waves move either sideways or up-down.

Is it possible for transverse waves to carry energy?

Transverse waves can carry energy during their movement.

If we observe the particle’s movement in a transverse wave, we find that they move perpendicularly to the wave movement. They produce crests and troughs; here, we can see that energy is being carried from left to right along with the motion.

Can transverse waves travel through fluids?

Fluids are a combination of both liquids and gases.

Since the fluids include both mediums, it won’t be easy to propagate transverse waves in that medium. Even liquid transverse waves do not find the medium suitable for the propagation of particles. We know that transverse waves always displace perpendicularly to the wave motion in any medium. Still, it is not possible in the case of the fluid medium.

Is it possible for all the transverse waves to travel without a medium?

Transverse waves always require some medium to move from place to place or object.

We already know that they are an essential component of mechanical waves that always require some matter or medium to displace from one point to another. Also, one fundamental point is that transverse waves need some solid medium to transport.

Is it possible for transverse waves to travel in gases?

Transverse waves can’t pass through the gaseous matter.

The particles traveling in a gaseous medium will face difficulty propagating transversely because the particles in gaseous matter won’t have a mechanical driving force in the direction that will be normal to the wave motion of the subject.

How can transverse waves travel through a void?

In the vacuum region, only the transverse waves can move only due to the path the particle in the transverse waves follows.

Under the transverse waves category, electromagnetic waves are included. The spectrum of electromagnetic always involves various waves that transmit through many regions. The main types of waves that come under this are visible and radio waves that usually have the most prolonged displacement of particles that move in the vacuum.

Also Read:

How to Calculate the Energy of Seismic Waves: A Comprehensive Guide

March 28, 2024March 22, 2022 by Core SME lambdageeks.com

Seismic waves, also known as earthquake waves, are vibrations that travel through the Earth’s crust as a result of an earthquake or other geological phenomena. These waves carry energy, which can be calculated to understand the magnitude and impact of an earthquake. In this blog post, we will explore how to calculate the energy of … Read more

9 Examples Of Electromagnetic Waves: Detailed Explanations

January 21, 2024March 19, 2022 by Abhishek

This article discusses about examples of electromagnetic waves. As in the name suggests, the electromagnetic waves are related to both electricity and magnetism.

In this article we will be studying about different types of waves. After that we shall carry our discussion further to electromagnetic waves and its examples. Let us start with our discussion on electromagnetic waves first.

Radar waves
Solar energy
Heat sensors
Microwaves
Radiowaves
Television
Imaging bone structures
Kill bacteria
Used to observe visible world

What are electromagnetic waves?

Electromagnetic waves, the name itself suggests that these waves are related to both electricity and magnetic field.

These waves are formed by the vibrations taking place between electric and magnetic field. These type of waves constitute of oscillating electric field and magnetic field. We shall study more about waves in later sections of this article.

examples of electromagnetic waves — **Image: Polarised Electromagnetic Wave**

Image Credits: SuperManu, Onde electromagnetique, CC BY-SA 3.0

Types of waves

There are many types of waves. These are waves are sorted into two main groups of waves. The two main types of waves are given below-

Transverse waves– Transverse waves are those waves which oscillate along a path perpendicular to the direction of wave propagation. EM waves, ripples in water etc are some examples of transverse waves.
Longitudinal waves– Waves in which the medium vibrates parellely to the direction of wave propagation. The direction in which the medium is displaced has the same direction as that of direction of wave propagation.

Electromagnetic waves types

Even electromagnetic spectrum is divided in to seven other sub types. The classifiaction of these waves is done on the basis of their frequencies.

The different types of electromagnetic waves are given in the section below-

Gamma rays– The frequency range of gamma rays is >3×10^17 Hz and wavelength range is <1nm.
X rays– The frequency range of X rays is 3×10^16-3×10^17 and the wavelength ranges from 1 to 10 nm.
Ultraviolet rays– The frequency range of ultraviolet rays is 7.5×10^14-3×10^16 and the wavelength ranges from 10 to 400 nm.
Visible light- The frequency range of visible light is 4.3 x 10^14-7.5×10^14 and the wavelength ranges from 400 to 700 nm.
Infrared– The frequency range of infrared waves is 3×10^12 to 4.3×10^14 and the wavelength ranges from 700 to 10^5 nm.
Microwave– The frequency range of microwaves is 3×10^9 to 3×10^12 and the wavelength ranges from 10^5 to 10^8 nm.
Radio waves– The frequency range of radio waves is <3×10^9 and the wavelength range is >10^8 nm.

Electromagnetic waves example

Electromagnetic waves are used in everyday applications. Some of the examples where electromagnetic waves are used are given in the section given below-

Radar waves

Radar waves are used to detect enemy vessel near our vicinity. These waves are emitted by RADAR and are reflected back after striking to the enemy vessel. This vessel can be aircraft or submarine or any other human equipped vessel.

Solar energy

UV rays are used to generate electricity using solar panels. These rays after striking the panel generate an EMF inside the panel. A capacitor can then store the generated electricity. Night vision- Infrared waves are used to see objects during night time. Night vision camera and goggles are used for security purposes to catch thieves/ terrorists roaming in the dark.

Heat sensors

Heat sensors also use infrared waves. The heat spectrum is variable for different objects. Different objects emit different amounts of heat, this spectrum can be observed by using infrared waves.

Microwaves

Microwaves are used for heating food inside the microwave ovens. Even radar uses microwaves. Food is heated instantly after microwaves strike the food.

Radio waves

Radio waves are used for audio transmission by FM stations. They use these radio waves to broadcast their content.

Television

Television sets also use radio waves for the transmission of their content. We can see different shows on television with the help of these waves.

Imaging bone structures

X rays are used for imaging bone structures. These rays penetrate inside the human body and strikes the bones giving a luminiscent images of the same.

Kill bacterias

Gamma rays are used for killing bacterias in marshmallows and to sterilise medical equipments.

Used to observe visible world

Visible light spectrum is used by humans to see the world around us. Without this spectrum, we won’t be able to see objects around us.

Electromagnetic waves in the order of increasing wavelength

We have discussed in the above sections that EM waves are divided into seven types according to their frequency/wavelengths.

The different types of EM waves in increasing order is given in the section below-

Gamma ray, X ray, UV rays, Visible light, infrared rays, microwaves and radio waves.

How are electromagnetic waves formed?

Electromagnetic waves are the waves which are related to both electric field and magnetic field. These waves are produced with the help of both the types of fields.

When magnetic field and electric field come in contact with each other, electromagnetic waves are formed. Both magnetic and electric fields make ninety degrees with each other as well as to the direction of propagation of wave.

How are electromagnetic waves propagated?

There are different media of propagation of electromagnetic waves. These are given in the section below-

Ground waves– When the electromagnetic waves are transferred along the surface then it is called as ground wave propagation.
Space waves– When the electromagnetic waves travel through vacuum of space, then that type of propagation is called as space wave propagation. Light from sun and other stars travel using this mode of propagation.
Sky waves– Sky waves uses the principle of reflection. When electromagnetic waves are transmitted from the ground and are reflected back after striking ionosphere, then this type of propagation is known as sky wave propagation.

Properties of electromagnetic waves

The different properties of electromagnetic waves are given below-

These waves move with the speed of light.
These waves are transverse in nature, meaning the electric fields and magnetic fields are perpendicular to each other and the direction of wave propagation.
These waves can undergo interference and diffraction.
The EM waves cannot be deflected by electric field or magnetic field.
It is not necessary for a medium to exist for propagation of these waves. These waves can travel without the help of medium also.

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Amplitude of a Wave 2: A Comprehensive Guide

June 25, 2024March 3, 2022 by Core SME lambdageeks.com

The amplitude of a wave is a fundamental property that represents the maximum displacement of a particle from its equilibrium position. Understanding the amplitude of a wave is crucial in various fields, including physics, engineering, and signal processing. In this comprehensive guide, we will delve into the technical specifications, theorems, formulas, examples, and numerical problems … Read more

Does Longitudinal Wave Travel: A Comprehensive Guide

June 25, 2024February 19, 2022 by Raghavi Acharya

Longitudinal waves are a fundamental type of wave in physics, where the particles of the medium vibrate back and forth parallel to the direction of wave propagation. These waves are crucial in understanding various phenomena, from sound propagation to seismic activity. In this comprehensive guide, we will delve into the intricate details of longitudinal wave travel, exploring its characteristics, measurable properties, and practical applications.

Characteristics of Longitudinal Waves

Direction of Vibration

In a longitudinal wave, the particles of the medium vibrate back and forth along the same direction as the wave’s propagation. This is in contrast to transverse waves, where the particles oscillate perpendicular to the direction of wave travel.

Compression and Rarefaction

As a longitudinal wave propagates through a medium, the medium undergoes a cyclic process of compression and rarefaction. During compression, the particles of the medium are pushed closer together, resulting in a region of higher density. Conversely, during rarefaction, the particles spread out, creating a region of lower density.

Examples of Longitudinal Waves

Sound waves and seismic waves are two prominent examples of longitudinal waves. Sound waves, which are responsible for the transmission of auditory information, are longitudinal waves that propagate through various media, such as air, water, and solids. Seismic waves, generated by earthquakes or other seismic events, are also longitudinal waves that travel through the Earth’s interior.

Measurable Properties of Longitudinal Waves

Wavelength (λ)

The wavelength of a longitudinal wave is the distance between two consecutive points of the same phase, such as two adjacent compressions or rarefactions. The wavelength can be calculated using the formula:

λ = v / f

where v is the velocity of the wave and f is the frequency of the wave.

Frequency (f)

The frequency of a longitudinal wave is the number of wave cycles that pass a given point per unit of time, typically measured in hertz (Hz). Frequency is an important characteristic as it determines the pitch or tone of a sound wave.

Velocity (v)

The velocity of a longitudinal wave is the speed at which the wave propagates through the medium. The velocity of a longitudinal wave depends on the properties of the medium, such as its density and elasticity. For example, the velocity of sound waves in air is approximately 343 m/s at room temperature.

Example Calculation

Let’s consider a longitudinal wave traveling at a velocity of 10,000 m/s with a frequency of 4,000 Hz. We can calculate the wavelength of this wave using the formula:

λ = v / f
λ = 10,000 m/s / 4,000 Hz
λ = 2.5 m

Therefore, the wavelength of this longitudinal wave is 2.5 meters.

Factors Affecting Longitudinal Wave Propagation

Medium Properties

The properties of the medium through which a longitudinal wave travels can significantly influence the wave’s propagation. Factors such as the medium’s density, elasticity, and temperature can affect the wave’s velocity and attenuation.

Boundary Conditions

The boundaries of the medium, such as the interface between two different materials, can also impact the behavior of a longitudinal wave. Reflection, refraction, and diffraction can occur at these boundaries, leading to complex wave patterns.

Interference and Superposition

When multiple longitudinal waves interact, they can undergo interference, either constructive or destructive. The principle of superposition allows us to understand how these waves combine and influence the overall wave pattern.

Dispersion

In some media, the velocity of a longitudinal wave may depend on its frequency, leading to dispersion. This can result in the separation of a wave into its constituent frequencies, as observed in the propagation of seismic waves through the Earth’s interior.

Applications of Longitudinal Waves

Sound and Audio Technology

The propagation of sound waves, which are longitudinal waves, is the foundation of various audio technologies, such as music, speech communication, and ultrasound imaging.

Seismic Exploration

Longitudinal waves, known as primary (P) waves, are used in seismic exploration to study the Earth’s interior structure and detect geological features, such as oil and gas deposits.

Medical Imaging

Ultrasound imaging, which relies on the propagation of high-frequency longitudinal waves, is widely used in medical diagnostics to visualize internal organs and monitor fetal development.

Nondestructive Testing

Longitudinal waves are employed in nondestructive testing techniques, such as ultrasonic testing, to detect defects or flaws in materials without causing damage.

Conclusion

Longitudinal waves are a fundamental concept in physics, with a wide range of applications in various fields. By understanding the characteristics, measurable properties, and factors affecting the propagation of longitudinal waves, we can gain valuable insights into the behavior of these waves and their practical implications. This comprehensive guide has provided a detailed exploration of the intricacies of longitudinal wave travel, equipping you with the knowledge to delve deeper into this fascinating area of study.

References

The Physics Classroom. (n.d.). Sound as a Longitudinal Wave. Retrieved from https://www.physicsclassroom.com/class/sound/Lesson-1/Sound-as-a-Longitudinal-Wave
arXiv. (2024). How do longitudinal waves propagate transversely? Retrieved from https://arxiv.org/html/2406.15212v1
TeachEngineering. (n.d.). Waves and Wave Properties – Lesson. Retrieved from https://www.teachengineering.org/lessons/view/clem_waves_lesson02
ScienceDirect. (n.d.). Longitudinal Wave – an overview. Retrieved from https://www.sciencedirect.com/topics/engineering/longitudinal-wave
Study.com. (n.d.). Wavelength Formula & Calculation. Retrieved from https://study.com/learn/lesson/wavelength-formula-calculate.html
Nave, C. R. (n.d.). Longitudinal Waves. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/sound/longwave.html
Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers with Modern Physics (10th ed.). Cengage Learning.
Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers (6th ed.). W. H. Freeman.

How to Find the Amplitude of a Wave: A Comprehensive Guide

January 21, 2024February 16, 2022 by SAKSHI KM

In the world of waves, understanding their properties is crucial for various scientific and technological applications. One such property is the amplitude of a wave. The amplitude of a wave refers to the maximum displacement or distance from the equilibrium position of a wave. It plays a significant role in wave analysis and provides valuable insights into the behavior and characteristics of different types of waves.

How to Determine the Amplitude of a Wave

Image by Omegatron – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.

Definition of Amplitude in a Wave

The amplitude of a wave is a measure of its maximum displacement or distance from the equilibrium position. In simpler terms, it represents the height or strength of a wave. For example, in the case of an ocean wave, the amplitude would indicate the maximum height of the wave from its resting position.

The Importance of Amplitude in Wave Analysis

The amplitude of a wave is essential in understanding various aspects of wave behavior. It affects the energy carried by the wave, as waves with larger amplitudes typically carry more energy than those with smaller amplitudes. Additionally, the amplitude plays a role in determining the loudness of sound waves and the brightness of light waves.

The Formula to Calculate the Amplitude of a Wave

The amplitude of a wave can be calculated using the following formula:

$A = \frac{D}{2}$

Where:
– A represents the amplitude of the wave
– D is the maximum displacement or distance from the equilibrium position

The formula states that the amplitude of a wave is equal to half of its maximum displacement.

Worked Out Example: Calculating the Amplitude of a Wave

Let’s consider an example to understand how to calculate the amplitude of a wave. Suppose we have a transverse wave represented by the equation:

$y = 3 \sin(2x)$

To find the amplitude of this wave, we can observe that the coefficient of the sine function is 3. According to the formula, the amplitude (A) is equal to half of this coefficient:

$A = \frac{3}{2} = 1.5$

Therefore, the amplitude of this wave is 1.5.

Special Cases in Finding the Amplitude of a Wave

How to Determine the Amplitude of a Sine Wave

A sine wave is a smooth oscillation that follows a specific mathematical function. In a sine wave, the amplitude represents the maximum displacement from the equilibrium position. To determine the amplitude of a sine wave, we can directly read the coefficient of the sine function, following the formula mentioned earlier.

How to Measure the Amplitude of a Longitudinal Wave

In a longitudinal wave, the particles of the medium vibrate parallel to the direction of wave propagation. Determining the amplitude of a longitudinal wave can be more challenging than with transverse waves. One common method is to measure the maximum compression or rarefaction of the medium caused by the wave. This measurement would correspond to the amplitude of the longitudinal wave.

How to Find the Amplitude of a Sound Wave

Sound waves are longitudinal waves that require a medium to propagate. The amplitude of a sound wave corresponds to the variation in air pressure caused by the wave. In practical terms, the amplitude of a sound wave is often linked to the loudness or intensity of the sound. Instruments such as microphones can measure the amplitude of sound waves.

Worked Out Example: Finding the Amplitude of a Transverse Wave

Consider a transverse wave given by the equation:

$y = 2 \cos(3x - \frac{\pi}{4})$

To find the amplitude, we can observe that the coefficient of the cosine function is 2. According to the formula, the amplitude (A) is equal to half of this coefficient:

$A = \frac{2}{2} = 1$

Therefore, the amplitude of this transverse wave is 1.

Understanding the amplitude of a wave provides valuable insights into the behavior and characteristics of different types of waves. Whether it is a sine wave, longitudinal wave, or sound wave, the amplitude plays a crucial role in analyzing and interpreting wave properties. By following the appropriate formulas and techniques, we can calculate and measure the amplitude of waves accurately. So, the next time you encounter a wave, remember to find its amplitude to gain a deeper understanding of its nature.

Numerical Problems on how to find the amplitude of a wave

Problem 1:

A wave has a maximum displacement of 5 cm and a wavelength of 10 cm. Find the amplitude of the wave.

Solution:

Given:
Maximum displacement (A) = 5 cm
Wavelength (λ) = 10 cm

The amplitude (A) of a wave can be found using the formula:

$A = \frac{{\text{{Maximum displacement}}}}{2}$

Substituting the given values into the formula, we get:

$A = \frac{5}{2} = 2.5 \, \text{cm}$

Therefore, the amplitude of the wave is 2.5 cm.

Problem 2:

Image by Dake – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.

The amplitude of a wave is 3 m and the frequency is 4 Hz. Find the velocity of the wave.

Solution:

Given:
Amplitude (A) = 3 m
Frequency (f) = 4 Hz

The velocity (v) of a wave can be determined using the formula:

$v = \lambda f$

where λ is the wavelength of the wave.

Since the wavelength (λ) can be calculated using the formula:

$\lambda = \frac{v}{f}$

Substituting the given values into the formula, we have:

$\lambda = \frac{3}{4} = 0.75 \, \text{m}$

Now, substituting the wavelength (λ) and frequency (f) into the velocity formula, we get:

$v = 0.75 \times 4 = 3 \, \text{m/s}$

Therefore, the velocity of the wave is 3 m/s.

Problem 3:

A wave has a velocity of 350 m/s and a frequency of 500 Hz. Determine the wavelength of the wave.

Solution:

Given:
Velocity (v) = 350 m/s
Frequency (f) = 500 Hz

The wavelength (λ) of a wave can be calculated using the formula:

$\lambda = \frac{v}{f}$

Substituting the given values into the formula, we get:

$\lambda = \frac{350}{500} = 0.7 \, \text{m}$

Therefore, the wavelength of the wave is 0.7 m.

Also Read:

Can Longitudinal Waves Travel Through A Vacuum: How, Why And Detailed Explanations

January 21, 2024February 15, 2022 by Raghavi Acharya

We will study in detail how longitudinal waves travel through a vacuum and the detailed explanations in this article.

Longitudinal waves are essential types of mechanical waves that always require a particular medium to travel. But in a vacuum, we can find no such medium that helps the longitudinal waves to propagate. Hence, they cannot travel through a vacuum because of the absence of any matter in it.

Let’s scroll into the article to know can longitudinal waves travel through a vacuum.

Longitudinal wave: Concept and insights

Longitudinal waves are one of the primary types of mechanical waves.

The simple way to define a longitudinal wave is a mechanical wave in which the position of the wave in the medium displaces in the same direction in which the propagation of the wave occurs.

To know the critical propagation medium of longitudinal waves.

Can longitudinal waves travel through a vacuum?

Longitudinal waves cannot move through a vacuum due to the lack of medium required for the propagation.

For any longitudinal wave to propagate, a medium is a must. Since the Vacuum does not contain any medium essential for the propagation of longitudinal waves, it cannot travel through Vacuum.

To understand the concept of movement of longitudinal waves in space.

Why does longitudinal waves cannot travel in space?

Space is a region where the medium will be absent. It is almost similar to Vacuum.

We have already read that longitudinal waves can move or travel only with the help of any medium. If the medium is absent, then it can’t propagate. Since space is similar to Vacuum, longitudinal waves cannot travel through it.

To understand the longitudinal wave propagation through various examples.

Examples of longitudinal waves that help to know the propagation of the wave in Vacuum

The critical longitudinal wave types include sound waves, tsunami waves, spring waves, etc. In detail, we will know why these longitudinal waves cannot travel in Vacuum.

Waves of Tsunami
Different sound waves
Waves during earthquakes or pressure waves
Spring waves

Waves of Tsunami

The waves that hit the seashore during the massive Tsunami are also examples of longitudinal waves. These waves create considerable destruction and cause several damages in the shore regions. Specific media such as air or water are required for these waves to propagate, and the atoms these waves vibrate and propagate in a parallel direction to the wave movement when they reach the shore. Since the Vacuum lacks the medium, longitudinal waves cannot travel in it.

Different sound waves

Sound waves are an actual longitudinal wave example. In general, the sound waves need a specific air medium to propagate and process the information to be heard by someone. The different sounds, such as while speaking, musical instruments, songs, etc., are traveled through a medium. It is the reason these longitudinal waves cannot pass through the Vacuum since it lacks the presence of matter.

Waves during earthquakes or pressure waves

The earthquake waves are also widely known as seismic-p waves. It occurs in the inner part of the earth. These waves require a particular medium to travel to the earth’s surface when pressurized. As soon as it reaches the surface with a bit of bump causing destruction, it is considered seismic s-waves. So, it is an actual longitudinal wave example. If there were a Vacuum region inside the earth, it would not have provided the medium that helps the wave travel.

Spring waves

While playing with a spring, certain waves will occur in it, resulting in propagation if you pull its ends. These waves require a specific medium or matter to propagate, and if knocked the spring in Vacuum, then there would be an absence of propagation due to the absence of matter. But in everyday surroundings, the spring waves are considered the best longitudinal wave example.

Conditions affecting the propagation of the longitudinal wave

The essential conditions to be considered in the propagation of waves are that help us to know can longitudinal waves travel through a medium are as follows,

Presence of medium
The velocity of longitudinal wave
Wave impedance
The density of the medium of propagation
The rigidity of the medium

To understand the various factors that help in studying longitudinal waves can travel through a medium.

Factors that help in the propagation of longitudinal waves

The different factors of longitudinal waves that help in the propagation through any medium are explained below,

The amplitude of the longitudinal wave

In any longitudinal wave, its amplitude will be considered to be the displacement from any point in the medium from the point of equilibrium.

Compression and Rarefraction of longitudinal wave

Both compression and rarefaction are the essential components of longitudinal waves. In the compression region, the waves are very far from one another, whereas the atoms will be nearer to one another in the compression region.

Period of longitudinal wave

The time for movement of the wave from the displacement of one wavelength is considered the period of a longitudinal wave.

The above given are essential factors to be considered in wave propagation.

Frequently Asked Questions | FAQs

On what medium does a longitudinal wave not travel?

Longitudinal waves can propagate through all types of matter or mediums like solids, liquids, and gases but are prohibited from passing through the Vacuum.

In general, all the longitudinal waves need some medium to propagate. The Vacuum is a medium where we find the absence of any matter that helps the mechanical waves, such as longitudinal waves, pass through it.

On What type of medium can longitudinal waves propagate?

Longitudinal waves can usually pass through all the types of matter that contain a medium.

While these longitudinal waves travel, all the particles present in them vibrate parallel to the wave propagation. The particle can vibrate in the medium, such as solids, liquids, and gases, which help the longitudinal waves to travel through it.

Why can longitudinal waves not travel through a vacuum?

All the vacuum region does not consist of any matter that helps propagation longitudinal waves.

All longitudinal waves need a particular medium to travel or for propagation. But in the case of a Vacuum, there will be the absence of a specific medium that helps the waves pass through it. It is why the longitudinal waves do not travel through any vacuum region.

Do longitudinal waves propagate through a liquid medium?

Longitudinal waves can propagate through all the liquid matter since it allows the particles to vibrate and travel.

A space that contains some matter helps all the types of longitudinal waves to travel through it. So, liquids and fluids are types of matter that surely help them pass through them by vibrating.

In what way do longitudinal waves travel through the air?

Air is one of the kinds of matter in which all the atoms are very loosely arranged together and help the waves propagate through them quickly.

Air provides a medium suitable for any longitudinal waves to pass through it. The atoms vibrate in an air medium in such a direction that it is parallel to the wave propagation; these vibrations are transferred to other atoms in the medium, making the propagation easy.

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What Is the Speed of a Transverse Wave: Why, How, Problems, Examples

January 21, 2024February 9, 2022 by Manish Naik

The article discusses about what is speed of a transverse wave with some solved problems and examples.

The particles within the transverse wave move perpendicular to wave propagating. When the wave moves, its particles oscillate from their equilibrium position, which we call the ‘speed of a transverse wave’. It depends on the wavelength and frequency properties of the transverse wave.

The particles oscillation from equilibrium or mean position sets up the properties of the transverse, and it is measured as the particle’s ‘displacement’ (s). The maximum displacement from their mean position gives rise to its ‘Amplitude‘ (denoted as A).

The peaks emerge above the mean position due to maximum displacement called ‘crest’, whereas the peaks emerge lower than the mean position due to maximum displacement called ‘trough’. The shape of the crest and trough is a natural process when transverse waves propagate.

So when we estimate the horizontal distance the transverse wave travels, we get another wave property called ‘Wavelength’, denoted by symbol lambda (λ). It is the distance between either two crests or two troughs; hence it is measured in a metre (m).

**What is the Speed of a Transverse Wave**

The time is taken by an entire wavelength or two successive crests to pass through a fixed point called ‘Period’ (denoted as T). Whereas the number of wavelengths travelling in one second through a given point is called ‘Frequency’ (denoted as f), and it has a measuring unit as Hertz (denoted by Hz).

Speed of a Transverse Wave Formula

The speed of a transverse wave is obtained from its properties like wavelength, frequency and period.

The distance travelled by a transverse wave in unit time describes its speed. Hence, the distance between two crests or troughs in the transverse wave is calculated as one wavelength, whereas the unit time is one period. Therefore, the speed of the transverse wave formula is the ratio of its wavelength to period.

Math

v = λ/t ……………..(*)

But as per definitions, the period (T) and frequency (f) are reciprocal. i.e., f = 1/T

Equation (*) becomes,

v = λ/T

The speed of a transverse wave formula is,

v = λ/f

What is the speed of a transverse wave, which has a wavelength of 50m and a frequency of 100Hz?

Given:

λ = 50m

f = 100Hz

To Find:

v =?

Formula:

v = λ/f

Solution:

The speed of a transverse wave is calculating as,

v = λ/f

Substituting all values,

v = 50 x 100

v = 500

The speed of a transverse wave is 500m/s.

If the sound wave has a frequency of 200Hz, what is its time period to pass successive wave crests? Also, calculate the speed of a sound wave if its wavelength is 80m.

Given:

f = 200Hz

λ = 80m

To Find:

T =?

v =?

Formula:

f =1/T

v = λ/f

Solution:

The time period of sound wave is calculated as,

f = 1/T

T= 1/f

Substituting values,

T= 1/200

T = 5 x 10^-3

T = 5ms

The time period of a transverse sound wave is 5ms.

The speed of a transverse wave is calculating as,

v =λf

Substituting all values,

v = 80 x 200

v = 1600

The speed of a sound waves is 1600m/s.

When the guitar string is plucked, it produces transverse waves. If the waves having a wavelength of 40m moves at 200m/s, what is the time period of waves?

Given:

λ = 40m

v = 200m/s

To Find:

T =?

Formula:

v = λf

f= 1/T

Solution:

First we calculate the frequency of transverse of wave as,

v = λf

f = v/λ

Substituting all values,

f = 200/40

f = 50

The frequency of the transverse wave produced on the guitar string is 50Hz.

The time period of transverse wave is calculated as,

T= 1/f

T= 1/50

T = 20 x 10^-3

The time period of a transverse wave is 20ms.

What is the Speed of a Transverse Wave on a Stretched String?

The speed of a transverse wave generated on a stretched string is the ratio of its tension and linear density quantities.

When we pluck the stretched string tied at both ends, it vibrates to create the number of sound waves as transverse waves. The sound waves move with higher speed on a stretched strings than other mediums because of the string’s high tension values and low mass per unit length.

The string is one of the flexible connectors that transmit the disturbance to both ends when stretched. The disturbance is reflected from both ends and creates sound waves on the string. Tension (denoted as T) is the main kay that makes the disturbance travel throughout the string. It is one of the types of force that transmits the applied force and prevents the flexible connector from breaking.

**Speed of a Transverse Wave on a Stretched Spring**

Even though string has different thicknesses, it is made of the same material. Its mass per unit length is what we termed as linear density (denoted as μ). So,

mu =m/I

Instead of its frequency, the speed of a transverse wave created on a stretched string depends on its tension and linear density.

“The transverse wave speed is directly proportional to the square root of tension (T) and inversely proportional to the square root of the linear density μ.”

v = √T/mu

The rope is also one of the flexible connectors like a string. Hence, the speed of a transverse wave formula for the rope is the same as for the stretched string.

Transverse Wave on a Rope — **Tension on the Stretched Rope**
(credit: shutterstock)

What is the speed of a transverse wave on a stretched string with a tension of 300N and a linear density of 0.15kg/m?

Given:

T = 300N

μ = 0.15kg/m

To Find:

v =?

Formula:

v = √T/mu

Solution:

The speed of a transverse wave is,

v = √T/mu

Substituting all values,

v =√300/0.15

v = √2000

v = 44.72

The speed of a transverse wave is 44.72m/s.

A guitar string has a mass of 2kg and 10m. What should be the tension on the string so that the speed of a sound waves equals 300m/s.

Given:

m = 2kg

l = 10m

v = 300m/s

To Find:

T =?

Formula:

v = √T/mu

Solution:

First we need to calculate the linear density as,

mu = m/I

Substituting all values,

mu = 2/10

mu = 0.2kg/m

The tension on string is calculated as,

v = √T/mu

Squaring both sides,

v² = T/mu

T = v²mu

Substituting all values,

T = 300² x 0.2

T = 900 x 0.2

T = 180

The tension on the string is 180N.

What is the tension on the rope of 5kg and 8m long on which the produced transverse wave travels 20m in 5s?

Given:

m = 5kg

l = 8m

d = 20m

t = 5s

To Find:

T =?

Formula:

v = √T/mu

Solution:

First we need to calculate the linear density as,

mu = m/I

Substituting all values,

mu = 5/8

mu = 0.62

The tension on the rope is calculated as,

v = √T/mu

But speed formula is v= d/t, hence

Squaring both sides,

20/5 = √T/0.62

4 = √T/0.62

Squaring both sides,

16 = √T/0.62

T = 16 x 0.62

T = 9.92

The tension on the rope is 9.92N.

Do all Transverse Waves have Same Speed?

All transverse waves have the same speed in vacuum only, not in medium.

Electromagnetic (EM) waves are transverse waves that move at the same vacuum speed, i.e., 3×10⁸m/s. But when it passes through any medium, its speed decreases as a wave-particle interacts with particles of the medium.

The permittivity or permeability quantity of the medium affects the constant speed of a transverse waves. Although the wave’s frequency stays intact in the medium, its wavelength varies slightly. That’s the reason when the white light passes through a dispersed medium like a prism; it splits into different colors as its speed changes into the prism.

“The amount of change in speed of a transverse waves is given by the formula of the index of refraction (n) as waves get refracted into the medium.”

Transverse Wave Refraction — **Transverse** Wave Refraction
(credit: shutterstock)

n = c/v

where c is the light speed in a vacuum.

v is the light speed in the medium.

What is the speed of a transverse wave in glass with the index of refraction as 1.5?

Given:

n = 1.5

c = 3×10⁸m/s

To Find:

v =?

Formula:

n = c/v

Solution:

The speed of a transverse wave in a glass is calculated as,

n = c/v

v = 3.8 x 10⁸/1.5

v = 2.53 x 10⁸

The speed of a transverse wave in the glass is 2.53 x 10⁸m/s.

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