Progressive waves

​​In a nutshell

A progressive wave carries energy between locations without transferring any matter. The two types of progressive waves are transverse and longitudinal. Electromagnetic waves are transverse waves which form a spectrum of wavelengths. The wave speed equation links wave speed with frequency and wavelength. 

Equations

Constants

Variable definitions

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Progressive waves

Waves are caused by oscillations (vibrations) of particles or fields at a source.

A progressive wave is a wave that carries energy between locations without transferring any matter. This means that the particles, in the medium the wave is travelling through, oscillate but do not travel along the wave.

A wave travelling through a medium causes the particles within in the medium to move from their equilibrium position. This displaced particle then feels a restoring force from its neighbouring particles and returns to its equilibrium position. The displaced particle also exerts a upwards force on its neighbours which cause them to displace. This continues in a chain.

Example

Oscillations of water waves travel along the surface of the water. An oscillating molecule of water will move up as the wave passes through. The displaced molecule attracts its neighbouring molecule upwards, whilst its neighbouring molecule pulls the displaced molecule downwards. This causes the original molecule to move down and the neighbouring molecule to move up, forming a transverse wave.

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Transverse and longitudinal waves

There are two types of progressive wave: transverse waves and longitudinal waves. The difference between them is their direction of oscillation.

Transverse waves

Transverse waves oscillate perpendicular (at $$90\degree$$) to the direction of energy transfer.

Note: The direction of energy transfer is the same as the direction of the wave's movement!

Longitudinal waves

Longitudinal waves oscillate parallel to the direction of energy transfer.

Wave speed equation

The wave speed equation relates the speed of the wave in the direction of travel to the frequency and wavelength of the wave.

​$$v = f\lambda$$

Note: Make sure to not get confused between the speed of the wave and the speed of the oscillating particles! The wave equation looks at the speed of the wave.

Example

A wave travels at a speed of $$525\,ms^{-1}$$ with a frequency of $$3.2\,Hz$$. What is the wavelength of the wave?

First, write out the quantities given and check they are in the correct form:

$$v = 525\,ms^{-1} \newline f = 3.2 \,Hz$$​​

Next, write down the equation you need to use:

$$\lambda = \dfrac{v}{f}$$​​

Then, substitute the values into the equation:

$$\lambda = \dfrac{525}{3.2} = 164.06...$$​​

Make sure to include units and round to the lowest number of significant figures of the values given in the question:

$$wavelength, \,\lambda = 160 \,m$$​​

$$\underline{The \space wavelength \space of \space the \space wave \space is \space 160\,ms^{-1}}$$.

Electromagnetic waves

An electromagnetic (EM) wave is a transverse wave which consists of an electric and magnetic field oscillating at right angles to each other.

Tip: An EM wave is a good to remember for an example of a transverse wave!

A. Direction of travel

The electromagnetic spectrum is the range of EM wavelengths. It goes from the longest wavelength, radio waves, to the shortest wavelength, gamma rays. 

A. Decreasing wavelength (values in $$m$$)​ B. Range of possible overlap of gamma and x-ray wavelengths 1. Radio waves 2. Microwaves 3. Infrared radiation 4. Ultraviolet radiation 5. X-rays 6. Gamma rays 7. Visible light (values in $$nm$$)​

Note: Visible light (the light humans can see) makes up only a small range of wavelengths of the electromagnetic spectrum!

All electromagnetic waves travel at the same speed through a vacuum. This speed is $$3.00\times 10^{8} \,ms^{-1}$$ and is written in equations as the constant $$c$$​. This is approximately the speed of an EM wave through air as well.

The wave speed equation for an electromagnetic wave can be rewritten as

​$$c = f\lambda$$

Example

An electromagnetic wave travels through a vacuum with a wavelength of  $$10^{-2}\,m$$.

a) What type of electromagnetic wave is this?

b) What is the frequency of the electromagnetic wave?

a) This is a microwave as it fits in the range of wavelengths in the microwave region of the electromagnetic spectrum.

b) First, write out the quantities given and check they're in the correct form:

$$\lambda = 10^{-2}\,m$$​​

Next, write down the equation you need to use:

$$f = \dfrac{c}{\lambda}$$​​

Then, substitute the values into the equation:

$$f = \dfrac{3.00\times 10^{8}}{10^{-2}} = 3\times10^{10}$$​​

Make sure to include the correct units and round to the lowest number of significant figures of the values given in the question:

$$frequency, \,f = 3 \times10^{10}\,Hz$$​​

$$\underline{The \space frequency \space of \space the \space microwave \space is\space \,3 \times 10^{10}\,Hz}$$.