# Transverse Wave

Even if we may not know what they are or what they're about, we've all heard of waves. We've at least all seen some waves at the beach, oceans waves that actually transmit energy rather than water, but have you ever thought about other kinds of waves you may not have noticed? Maybe waves smaller than we can see, or waves that you may not initially notice? Well, these waves come in different categories, and the kind we're looking at today is transverse waves, a very interesting type of wave. But what are transverse waves, how do they work, and what examples are there of them out there? Let's find out.

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## Transverse Wave Definition

Before we go into detail on the specifics of a transverse wave, let's first go over what a wave is exactly, in this context at least. A wave at its most general definition is the consistent and repeated motion of disturbances that travel from one area in space to another. Typically when we think of a wave, we imagine the standard up and down of a line, regular and identical, traveling from left to right. This isn't the case for every wave, as the highs and lows of a wave don't need to be identical every time, they don't need to exactly be up and down, and they don't necessarily have to move from left to right. Let's first define a transverse wave.

A transverse wave is one in which the oscillating particles move back and forth in a direction that is perpendicular to the motion of the wave.

Many other factors of a wave can change, but as long as this rule is followed by the wave, no matter what else changes, this is a transverse wave. The figure below illustrates a transverse wave, a water wave being a good example, where the water particles move up and down but the wave moves laterally toward the shore. The directions of the wave and the particles are perpendicular to each other.

The diagram represents the motion of a transverse wave as viewed from the side. The wave moves from left to right whilst the particles oscillate up and down. The two directions are perpendicular to each other, which is the requirement for a transverse wave, Wikimedia Commons

## Transverse Wave Properties

The main property that separates transverse waves from all other kinds of waves is the fact that they oscillate perpendicular to their direction of motion. But this isn't the only property a transverse wave has. Firstly, a transverse wave will always have a distance between its highs and lows, or crests and troughs respectively. The central position, about which the particles are oscillating, is known as the rest or equilibrium position. The distance that a particle is from the equilibrium position is known as its displacement. The maximum displacement occurs when a particle is at a crest or a trough and is called the amplitude of the wave. The distance between two successive crests or troughs is known as the wavelength of the wave. The period of a transverse wave is the time that elapses for an entire wavelength to complete, and the frequency is how often these periods occur in the space of one second. All of these properties are labeled below.

A transverse wave with all properties labelled.

## Difference between Transverse Waves and Longitudinal Waves

If transverse waves exist on one side of a coin, then certainly on the other side of that coin would be longitudinal waves. Longitudinal waves are very similar to transverse waves, with one key difference being what sets them apart. While particles in transverse waves oscillate perpendicular to the direction of motion, particles in longitudinal waves will move parallel to the direction of motion of the wave. This is the main property that sets these two waves apart, but this difference also leads to other differences between the two of them. A good example of longitudinal waves is sound waves, which push forward particles in the air in the same direction as the direction in which the sound wave is traveling.

As a transverse wave oscillates up and down while traveling left and right, it acts in two different dimensions. This isn't the case for longitudinal waves, since they don't act up and down, only ever left and right. This means that longitudinal waves only ever act in a single dimension.

Longitudinal waves can be created within any state of matter, be it solid, liquid or gas. Transverse waves don't have the same ability, they can be created in solids and on the surface of a liquid, but they can't be produced in gases whatsoever.

Finally, while we know that transverse waves have crests and troughs, since longitudinal waves don't act up or down, they don't have these. Instead, they have periods in their wave with more and less compression, the higher points of this being known as compressions, and the lower points being known as rarefactions. The image below shows a comparison between a transverse wave and a longitudinal wave. The longitudinal wave is set up on a slinky. Each loop of the slinky oscillates left and right and the wave travels parallel to this (either left or right).

This image shows the difference between transverse waves and longitudinal waves, Flickr.com

## Examples of Transverse Waves

So we know what transverse waves are, and what they do. But where can we find them, and how are they used? Well, we already touched on possibly the most important example of a transverse wave, light waves. All types of visible light are comprised of incredibly tiny transverse waves that travel right into your eyes, allowing you to see. As well as just light on the visible spectrum, all waves on the electromagnetic spectrum, from ultraviolet, and infrared, to x-rays and gamma rays, all of these are transverse waves.

Another great example of transverse waves is something you can try with any body of water. If you throw a pebble in, or simply poke the surface with your finger, you'll notice ripples emerging from the point of contact on the water. These ripples are transverse waves, the top of the ripple being the crests, with the path of travel being directed away from the point of contact. Because of this, we can imagine these ripples as sort of tiny waves.

Speaking of waves, enormous tsunami waves can be considered both transverse waves, and longitudinal waves, depending on which part of the waves lifecycle you're observing. At the beginning of a tsunami forming, it is a transverse wave, an earthquake underwater, shifting its energy to the water, and the wave moves as such until it reaches the surface, where it becomes longitudinal. The image below shows the transverse nature of a tsunami or tidal wave.

An example of a tsunami acting as a transverse wave. Wikimedia Commons

Finally, and as we're talking about earthquakes, these natural disasters are also good examples of transverse waves or at least one part of their process. "S" waves, what we know as the rapid up and down motion we experience during an earthquake, is a transverse wave. As the energy travels outward from the epicenter and parallel to the Earth's surface, the crest and troughs oscillate rock and ground up and down, causing this effect.

## The Transverse Wave Equation

Transverse waves possess many properties and variables to be determined. As a result, one single equation isn't going to give us all the data we require to fully understand a single transverse wave. However, here are two particularly useful equations:

$f=\frac{1}{T}$

This equation is used to calculate the frequency $$f$$ of a transverse wave, measured in Hertz ($$\mathrm{Hz}$$). The variable $$\mathrm{T}$$ is known as the period of the wave, which is the time taken for the wave to complete a full cycle, from the start of a crest to the end of the proceeding trough. This is measured in seconds ($$\mathrm{s}$$).

$v=f \lambda$

This final equation is used to calculate the speed of a wave, and how quickly it travels in a specific direction, measured in meters per second ($$\mathrm{m/s}$$). The variable $$\lambda$$ is known as the wavelength of the wave, which is the physical distance between the start of one cycle and the start of the proceeding cycle. This is measured in meters ($$\mathrm{m}$$).

A transverse wave has a time period of $$0.5 \, \mathrm{s}$$, and a wavelength of $$2.0 \, \mathrm{m}$$. What is the speed of this wave?

Solution

First, we need to combine our equations to gather all of the terms that we need. Combining them gives us this equation:

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

Inputting our values for the time period and the wavelength gives us this:

$$$\begin{split} v&=\frac{2.0\, \mathrm{m}}{0.5\, \mathrm{s}} \\\\ &=4.0 \, \mathrm{m/s} \end{split}$$$

The speed of this wave is $$4.0 \, \mathrm{m/s}$$.

## Transverse Wave - Key takeaways

• Transverse waves are waves in which the vibrating particles oscillate perpendicular to the wave's path of travel.
• The properties of transverse waves include displacement, amplitude, frequency, wavelength, and period.
• There are a few differences between transverse and longitudinal waves, including the state of matter they can be produced in, and the dimensions in which they act.
• There are many great examples of transverse waves we experience in life, including light waves, ripples in water, and earthquakes.
• The following equation can be used to calculate the speed of a wave: $$v=f \lambda$$.

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##### Frequently Asked Questions about Transverse Wave

What is a transverse wave?

A transverse wave is a wave that oscillates perpendicular to the path of travel.

What is an example of Transverse Wave?

An example of a transverse wave is a light wave.

What is the difference between transverse waves and longitudinal waves?

The difference between a transverse wave and a perpendicular wave is the direction in which they oscillate, transverse waves oscillate perpendicular to the path of travel, whereas longitudinal waves oscillate parallel to the path of travel.

What are the characteristics of Transverse Waves?

The characteristics of transverse waves are their crests and troughs, as well as their ability to be polarized.

What is the formula and equation for Transverse Waves?

The formulas and equations for transverse waves are that frequency is equal to one over the period of the wave, and velocity of the wave is equal to the frequency multiplied by the wavelength of the wave.

## Test your knowledge with multiple choice flashcards

Why does light experience the Doppler effect?

What is the main qualitative difference between the Doppler effects in light and in sound?

If two people are moving toward each other, what Doppler shift is at play?

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