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Properties of Waves

If you're a bit confused about different types of waves and the various words used to describe them then you have come to the right place! Waves are a type of energy pathway and are one of the ways how energy can be transferred between energy stores. They do not transport matter, only energy. A wave is essentially an oscillation…

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Properties of Waves

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Jetzt kostenlos anmeldenIf you're a bit confused about different types of waves and the various words used to describe them then you have come to the right place! Waves are a type of **energy pathway** and are one of the ways how energy can be transferred between **energy** **stores**. They do *not* transport matter, only energy. A wave is essentially an **oscillation** or a **vibration** about the **rest**** ****position**,** **transmitted** **through a medium or a vacuum. Scientists can define the nature and behaviour of these waves using wave property terms, such as **amplitude**, **frequency**, **period,** and **wavelength**. This article will help you understand the science behind all of these terms.

Waves can be either **transverse **or** longitudinal**. The difference depends on the direction of the wave's oscillations. If the oscillations of the wave are **perpendicular** (right angle) to the direction of travel then the wave is transverse. However, if the oscillations are **parallel** (same direction) to the wave's direction of travel then the wave is longitudinal.

One example of a transverse wave is the electromagnetic wave, where both the electric and magnetic components of the wave oscillate perpendicular to the direction of travel. Sound waves are a typical example of a longitudinal wave, where the particles vibrate back and forth parallel to the wave's direction of travel.

Another important distinction when discussing waves is whether a wave is **mechanical** or **non-mechanical**. The main difference between these two types of waves is if the wave requires a medium to travel through or not. Light can travel through the **vacuum** of space, which means they are non-mechanical waves: they do not need a medium to travel. **A****ll** electromagnetic waves are different types of light, encompassing the entire electromagnetic spectrum from radio waves to visible light to gamma rays. Meanwhile, mechanical waves require a **medium** to travel through. The medium could be any solid, liquid, or gas, such as iron, water, or air.

The wave **frequency** is defined as the number of full waves passing an arbitrary point in space every second.

The wave **period** is the time taken for just one full wave to pass a point.

Waves with **shorter** periods will have **higher** frequencies, as more waves can pass through a point every second. On the other hand, waves with a **longer** period would have **lower** frequencies, because fewer waves can pass through a point every second.

Below is a formula used to calculate the frequency and the period of a wave

\[ f = \frac{1}{T}\,,\]

where \(f\) is the frequency of the wave and\(T\) is the period of the wave (s). In words, the equation above reads

\[ frequency = \frac{1}{time \, period}\,.\]

**Question 1**

A wave has a period of 0.005 seconds. What is the wave's frequency?

**Answer 1**

Use the formula relating wave frequency and period

\[ f = \frac{1}{T} = \frac{1}{0.005 \, \mathrm s} = 200 \, \mathrm{Hz}\,.\]

**Question 2**

If 400 full waves of a wave pass an arbitrary point in space in one second, how long is the period of this wave?

**Answer 2**

If 400 full waves per second pass a point, we have a wave frequency of 400 \(\mathrm{Hz}\). Rearrange the formula given earlier to make the period the subject

\[ T = \frac{1}{f} = \frac{1}{400 \, \mathrm{Hz}} = 0.0025 \, \mathrm s \,.\]

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 3**

The vertical displacement between the crest and trough of a water wave is 0.5 metres. What is the wave's amplitude?

**Answer 3**

Wave 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 \( 0.5 \, \mathrm m\) displacement between the crest and the trough by 2 to calculate the amplitude of the wave, which is \( 0.25 \, \mathrm m\).

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 0.01 metres. What is the total length of 10 wavelengths?

**Answer 4 **

The distance between two consecutive wave crests is equal to one wavelength. The length of 10 wavelengths means you must multiply this number by 10, so the answer to the question is

\[ 0.01 \mathrm m \times 10 = 0.1 \, \mathrm m\,.\]

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

\[ h = 2 A\,.\]

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.

A very useful equation to know when solving wave problems is the **wave speed** equation. This equation is used to calculate the speed that a wave is travelling at, using the product of the wave's frequency and its wavelength

\[ v = f \lambda \,,\]

where \(v\) is the wave speed (\( \mathrm m/ \mathrm s\)), \(f\) is the frequency (\(\mathrm{Hz}\)), and\(\lambda\) is the wavelength (\( \mathrm m\)). In words, this equation is

\[ wave \, speed = frequency \times wavelength \,.\]

The speed of a wave is **constant** if the medium the wave travels through is also **constant**. For instance, the speed of sound in air with a temperature of 20 \(° \mathrm C\) at sea level is approximately 343 \(\mathrm m/ \mathrm s\). Using the wave equation, we can see that **increasing** the frequency of a wave will **decrease** its wavelength proportionally. The opposite is also true! By **decreasing** the frequency of a wave then its wavelength will **increase** proportionally. This means the only way to change the speed of a wave, is to change the medium it travels through! Summarising, we have

\[ f \uparrow = \lambda \downarrow \, as \, f \lambda= constant \,.\]

Consider a sound wave travelling from air into the water. The sound waves that aren't reflected at the water's surface will become heavily distorted. The speed of sound in water is approximately 1480 \( \mathrm m/\mathrm s\), a factor of about greater than in air. This is partially due to the increased density of the water medium compared to air. The sound waves can travel faster in a denser medium as it is easier for particles to bump into each other when oscillating/vibrating.

**Question 5 **

A wave has a frequency of 200 \(\mathrm {Hz}\) and a wavelength of 25 \(\mathrm{mm}\). What is the wave speed?

**Answer 5 **

Convert \( 25 \, \mathrm{mm}\) into standard units, which reads \( 0.025 \, \mathrm{m}\), then use the wave speed equation to determine the wave speed as follows:

\[ v = f \lambda = 200 \, \mathrm{Hz} \times 0.025 \mathrm{m} = 5 \, \mathrm{m}/\mathrm{s} \,.\]

We conclude that the wave speed is \( 5 \,\mathrm m/ \mathrm s\).

**Question 6 **

A wave propagates through a medium with a wavelength of \( 30\, \mathrm{cm}\). 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, \( constant = f \lambda\). If you double the frequency of a wave then you must halve its wavelength for the speed to remain constant, as follows:

\[constant = 2 f \times \lambda/2 \,.\]

Therefore, the new wavelength would be \( 15 \,\mathrm{cm}\), or \(0.15 \,\mathrm{m}\).

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.

- Waves act as an energy pathway, which is a way to transfer energy between energy stores.
- A wave is a vibration/oscillation about the rest position, transmitted through a medium or a vacuum.
- If the wave's oscillations are perpendicular to the direction of travel then they are transverse waves. However, if the wave's oscillations are parallel to the direction of travel then they are longitudinal waves.
- Mechanical waves require a medium to travel through, while non-mechanical waves can travel through a vacuum, like electromagnetic (light) waves.
- Wave frequency is the number of full waves that pass an arbitrary point every second.
- 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.
- Wavelength is the length of one complete wave, typically measured crest-to-crest.
- The wave speed equation is$v=f\lambda $, and the wave speed is constant in the same medium.
- When two waves superimpose in phase with each other it causes constructive interference, two waves out of phase will create destructive interference.

- Fig. 1 - EM-Wave.gif (https://commons.wikimedia.org/wiki/File:EM-Wave.gif) by And1mu is licensed by CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/deed.en)
- Fig. 2 - Onde compression impulsion 1d 30 petit.gif (https://commons.wikimedia.org/wiki/File:Onde_compression_impulsion_1d_30_petit.gif) by Christophe Dang Ngoc Chan (cdang) (https://commons.wikimedia.org/wiki/User:Cdang) is licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/deed.en)
- Fig. 4 - Sine wave amplitude.svg (https://commons.wikimedia.org/wiki/File:Sine_wave_amplitude.svg) by Kraaiennest is licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/)
- Fig. 5 - Interference of two waves.svg (https://commons.wikimedia.org/wiki/File:Interference_of_two_waves.svg) by Haade (https://commons.wikimedia.org/wiki/User:Haade) is licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/)

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.

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

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