# Longitudinal and Transverse Waves

Waves are disturbances that propagate in space and time. A function of space and depending on time, they are thus dynamical entities. Importantly, waves do not necessarily need a material medium to propagate (electromagnetic waves would be an example of this), although this is usually the case, especially for most longitudinal waves.

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Periodic waves are waves with a repetitive pattern, usually in space. While, for instance, ocean waves (a counterexample) are not perfectly timed to appear on a beach at regular intervals, and their spacing, therefore, is not always the same either, when we throw a rock in a lake, the spacing between the water waves is almost exactly the same, although, of course, the disturbance does not last forever.

We must also remember that waves do not always displace the matter of the medium in which they are propagating. While ocean waves do displace water, vibrations on a string do not replace any matter, as the string remains in its position.

The main characteristics of periodic waves are:

• Wavelength: the length of each of the repeated patterns in the wave, which is usually denoted by λ.
• Frequency: the number of wavelengths completed per unit of time, which is usually denoted by f. Knowing the velocity v at which the wave travels, frequency and wavelength are related through the following equation:

$v = f \cdot \lambda$

• Amplitude: the length of the displacement caused by the wave. As we are going to see, this may be transverse, longitudinal, or a combination of both.
• Period: denoted by T, this is the time it takes for a wave to complete a wavelength. It is the inverse of the frequency:

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

• Phase: usually denoted by φ, this is derived from the mathematical description of the wave. It is a measure of the state of oscillation of a point. If two points are a wavelength apart, they are in phase since they are making the exact same movements. If two points are half a wavelength apart, they are said to be in ‘opposition of phase’ because they are making the opposite movements. The phase is the measure of the similitude of the points of a wave. It has a value between 0 and 2π. Whenever a point completes a wavelength, the number resets from 2π to 0.

See the following images of a periodic and a non-periodic wave:

Figure 1. Different types of periodic waves. The length after which a shape is repeated is called "wavelength". Source: Genttrit, Wikimedia Commons (CC BY-SA 3.0).

Figure 2. A Gaussian wave packet, an example of a non-stationary transverse wave. Source: Mathphysman, Wikimedia Commons (CC BY-SA 4.0).

Independent of their nature, waves transfer energy from one space point to another. The intensity and efficiency of this process depend on the various characteristics of the wave that we have already explored.

For instance, the intensity of a light source depends on the amplitude of the wave: the bigger the amplitude, the brighter the signal. However, this is an extensive measure in that doubling the number of lightbulbs would give us twice the amplitude. On the other hand, we find that the frequency is also related to the energy since it is a sign of the amount of movement the wave carries with it. For light radiation, this translates into the fact that blue and violet light is more energetic than yellow or red light.

## What are longitudinal and transverse waves?

We are now going to discuss the main characteristics of longitudinal and transverse waves.

### Transverse waves

Transverse waves are characterised by the fact that the displacement caused by them is perpendicular to the direction of their movement. The most famous example of a transverse wave is light itself. See the following figure for a visual representation of two periodic transverse waves:

Figure 3. Two transverse waves (pink and blue). The displacement caused by them is perpendicular to their direction (green). Source: pixabay.

In the case of transverse waves, their wavelength determines their energy. In light radiation, wavelength (which is inversely related to frequency) has to do with colour. For instance, there are wavelength thresholds for the light we can actually see. Longer wavelengths correspond to radio radiation, like what we use for the radio to work, while shorter wavelengths correspond to many others like microwaves.

### Longitudinal waves

Longitudinal waves, on the other hand, are characterised by the fact that the displacement they generate is in the same direction as their movement. We may think of the movement of a spring that has been stretched and released. The key aspect here is that the direction is much more restricted and that the movement generates changes in density (provided there is a material medium) since some regions will be either more compressed or more stretched. See the following figure for a visual representation of a longitudinal wave:

Figure 5. A longitudinal wave illustrated by the movement of a spring. Source: Zappys Technology Solutions, Flickr (CC BY 2.0).

## Examples of longitudinal and transverse waves

To conclude, we are going to analyse some of the most important examples of transverse and longitudinal waves and their properties.

As we saw, sound and light waves are very good examples of longitudinal and transverse waves, respectively. However, we are now going to consider a more visual example, which will allow us to understand some of their differences. Earthquakes are essentially disturbances generated in the inner layers of the earth that propagate until they reach the surface. The waves that are generated are particular in that, as they propagate on some solid mediums, the displacements they cause are permanent compared to the displacements caused in a fluid medium such as water.

We distinguish between:

• Primary waves/P-waves, which are longitudinal waves that travel approximately at the speed of sound and can move through any material, solid or liquid.
• Secondary waves/S-waves, which are transverse waves that travel at around 60% speed of sound and can move only through solid materials. This happens because the sheer forces in charge of transferring the wave’s disturbance do not exist in fluids or gasses.

Other examples of transverse waves include the vibrations in a guitar string or those generated in a regular string while one of its ends is being pulled up and down. Examples of longitudinal waves can be found in tsunami waves, which do have a transverse component but are mainly displacing water in the direction of their movement. Another example concerns ultrasound waves used, for instance, in pregnancy procedures, which is a good example in which both transverse and longitudinal components can be observed.

## Key takeaways

• There are two types of waves according to their displacement direction with respect to their direction of movement: longitudinal and transverse waves.

• Transverse waves comprise the most relevant examples in physics. Usually, they do not displace matter in a permanent way, and their properties, such as frequency and amplitude, are easily visualised.

• Longitudinal waves usually have to do with matter transferring the movement of the wave to nearby particles in a pressure-like way. This happens, for instance, with the sound or with tsunami waves.

• Unless we are considering very fundamental phenomena, such as electromagnetism and its waves, we find that waves have both longitudinal and transverse components.

#### Flashcards inLongitudinal and Transverse Waves 16

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What is the difference between longitudinal and transverse waves?

Longitudinal waves are waves whose displacement occurs in the direction in which the wave is also moving. In transverse waves, the displacement occurs in a direction perpendicular to the direction of movement.

How are longitudinal and transverse waves similar?

They are both types of waves, so they share characteristics, such as amplitude, period, frequency, wavelength, etc.

What are longitudinal and transverse waves?

Longitudinal and transverse waves are two types of waves and thus disturbances that propagate through time and space. The difference comes from the direction towards which the disturbance occurs.

Are electromagnetic waves longitudinal? And what about surface waves?

Electromagnetic waves are, in almost all media, transverse waves. Surface waves are transverse waves generated by an earthquake whose source is close to the surface of the earth. There are two types of surface waves, i.e., Rayleigh waves (vertical with respect to the earth’s plane) and Love waves (horizontal with respect to the earth’s plane).

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