# Properties of Waves

## Different types of waves

If you're wondering about waves, there are two types: transverse and longitudinal. It all depends on which way the wave is moving. If the wave moves up and down, but the vibrations are side to side, that's a transverse wave. But if the wave moves back and forth, and the vibrations are in the same direction, that's a longitudinal wave.

You can find two kinds of waves: transverse and longitudinal. Electromagnetic waves are one example of a transverse wave, where the wave moves perpendicular to the electric and magnetic fields. Check out the diagram above to see a woman creating a transverse wave in a slinky by moving the first coil up and down. Sound waves are an example of a longitudinal wave, where the particles move back and forth in the same direction as the wave. Wave frequency measures how many waves pass a point in space every second. The wave period is how long it takes for one complete wave to pass a point. Higher frequency waves have shorter periods, meaning more waves pass a point in a second. Lower frequency waves have longer periods, meaning fewer waves pass a point in a second.

Below is a formula used to calculate the frequency and the period of a wave whereis the frequency of the wave andis the period of the waveIn words, the equation above reads.

Question 1 A wave has a period of. What is the wave's frequency?

Answer 1Use the formula relating wave frequency and period.

Question 2 If full waves of a wave pass an arbitrary point in space in one second, how long is the period of this wave?

Answer 2Iffull waves per second pass a point, we have a wave frequency of. Rearrange the formula given earlier to make the period the subject.

## Wave amplitude

Below you can see a simple diagram of a wave. It has several labels that help us identify wave characteristics with wave terms.

The wave crest (or peak) is the highest point of oscillation above the rest position, while the trough is the lowest point of oscillation below the rest position. The amplitude of a wave is the maximum displacement between the rest position and its crest.

Alternatively, you could measure the maximum displacement between the rest position and the trough as well to get the amplitude of the wave.

The wave amplitude can help inform us about how much energy is in a wave. For example, big (tall) water waves carry more energy than little waves, as you might have experienced yourself. Another example is that an electromagnetic (light) wave with a high amplitude will be brighter than a dimmer, low amplitude wave. Similarly, a sound wave with a high amplitude will be louder than a wave with a lower amplitude.

Question 3The vertical displacement between the crest and trough of a water wave is. What is the wave's amplitude? Answer 3Wave amplitude is only measured between the crest and the rest position, or the trough and the rest position. The crest and trough of the wave have an equal displacement from the rest position. Therefore, you can divide the displacement between the crest and the trough byto calculate the amplitude of the wave, which is.

## What is wavelength

You can also observe that one full wavelength is the length of one complete cycle of the wave, most easily measured either crest-to-crest or trough-to-trough. Both wave amplitude and wavelength are measured in units of distance, with the standard unit as metres.

Question 4

The distance between two consecutive wave crests is. What is the total length of wavelengths?

The distance between two consecutive wave crests is equal to one wavelength. The length of wavelengths means you must multiply this number by,

so the answer to the question is

The total vertical displacement between the crest and the trough of a wave is actually a wave property known as wave height, which we measure in. Wave height is a particularly useful concept in coastal science. It is equal to twice the wave amplitude,.

Wave speed and phase

This section will help you to understand the slightly more complex concepts of wave speed, phase, and interference. Other wave properties previously discussed within this article (wave amplitude, wavelength, frequency, and wavelength) should all be understood before continuing.

## Wave Speed

The wave speed equation is a useful tool for solving wave problems. It calculates the speed that a wave is travelling at, using the product of the wave's frequency and its wavelength, where v is the wave f the frequency, and λ (lambda) is the wavelength. This equation is based on the fact that the speed of a wave is constant if the medium it travels through is also constant. For example, the speed of sound in air at sea level with a temperature of 20°C is approximately 343 meters per second. Changing the frequency of a wave will proportionally change its wavelength, but the only way to change the speed of a wave is to change the medium it travels through. For instance, sound waves travelling from air into water will be heavily distorted because the speed of sound in water is about 4.3 times greater than in air due to the increased density of the water medium. This makes it easier for particles to bump into each other when oscillating or vibrating.

Question 5 A wave has a frequency of and a wavelength of. What is the wave speed?

Answer 5 Convertinto standard units, which reads, then use the wave speed equation to determine the wave speed as follows:.We conclude that the wave speed is.

Question 6 A wave propagates through a medium with a wavelength of. In the same medium, what would the wavelength be if a new wave had double its frequency?Answer 6 The speed of a wave is constant in the same medium,. If you double the frequency of a wave then you must halve its wavelength for the speed to remain constant, as follows: Therefore, the new wavelength would be, or.

### Wave phase and interference

More than one wave can occupy the same position in space at the same time. If two waves coincide when their peaks and troughs match completely, then they are in phase with each other. This is called constructive interference. The two waves superimpose on each other, increasing the total wave amplitude. However, if two waves coincide where the peaks of one wave meet the troughs of another wave, then they are considered to be out of phase. The waves destructively interfere with each other, resulting in zero amplitude.

## Properties of Waves - Key takeaways

Waves are a means of transferring energy between energy stores. They are vibrations or oscillations that are transmitted through a medium or a vacuum. Waves can be categorized as either transverse waves, where oscillations are perpendicular to the direction of travel, or longitudinal waves, where the oscillations are parallel to the direction of travel. Mechanical waves require a medium to travel through, while non-mechanical waves, such as electromagnetic (light) waves, can travel through a vacuum. Wave frequency is the number of full waves that pass an arbitrary point second while wave period is the time for exactly one full wave to pass a point. Wave amplitude is the displacement between the crest (or trough) and the rest position, and wavelength is the length of one complete wave, typically measured crest-to-crest. The wave speed equation, which is , shows that the wave speed is constant in the same medium. When two waves superimpose in phase with each other, it causes constructive interference, while two waves out of phase will create destructive interference.

## Properties of Waves

What is wave amplitude?

The wave amplitude is the maximum displacement between the rest position and the wave's crest (or trough). Wave amplitude can help inform us of how much energy is in a wave.

What is an example of wave frequency?

Imagine an electromagnetic (light) wave. An EM wave with a very high frequency would have many full waves passing an arbitrary point per second. It would be either an x-ray or gamma-ray and it acts differently to a low-frequency wave, such as an infrared or radio wave.

What is wave period?

A wave period is the time taken for just one full wave to pass a point in space. Waves with shorter periods will have higher frequencies, as more waves can pass through a point every second.

What is a wavelength?

One full wavelength is the length of one complete cycle of the wave, typically measured crest-to-crest. It is measured in units of distance or metres.

What is speed and phase in waves?

Wave speed is simply the speed a wave crest is travelling at. It can be calculated using the product of the wave's frequency and wavelength. The phase of two waves describes the offset between two waves occupying the same point in space. In-phase waves have peaks and troughs that align completely and constructively interfere. Out-of-phase waves have the peaks of one wave meet the troughs of the second wave, causing destructive interference.

What are the properties of electromagnetic waves?

Electromagnetic waves are transverse waves, where the electric and magnetic components of the wave oscillate perpendicular (at a right angle) to its direction of travel. Electromagnetic waves are light waves.

What are the properties of longitudinal waves?

Longitudinal waves oscillate parallel (same direction) as the wave's direction of travel