On this page we will examine the wave phenomena of reflection, refraction, interference, diffraction and polarisation, as well as the concept of standing (or stationary) waves.

To show these in a visual way we will use a ripple tank simulation. Wave simulations use the same mathematical equations that are used to model real waves. Therefore they have have the same properties.

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Reflection

When a wave hits a boundary or change in medium, it reflects back. Each point on the boundary behaves like a small wavelet source.

the angle of incidence = the angle of reflection

Refraction

When a wave travels into a more dense medium, it slows down. This causes the wave to change direction.

\({\sin i\over \sin r}={v_1\over v_2}\)

Interference

When two balls collide, they bounce off each other. When two waves collide, they pass through each other.

Where the waves overlap the amplitudes add, this is called superposition. This results in interference effects.

Diffraction

When a wave passes through an opening in a barrier, it spreads out. Diffraction is optimised where the width of the opening is approximately equal in size to the wavelength.

Stretch for 7

Polarisation

A wave in a guitar string, like many examples of waves, oscillates in all directions.

A polarised wave only oscillates in one direction.

Standing waves

A standing wave is formed when two waves, of equal frequency and amplitude, travelling in opposite directions interfere.

v_{1}/v_{2} = sin i_{1}/sin i_{2 }= sin 30°/sin70°

A plane wave passes across the boundary from one medium to another as shown.

The ratio velocity in medium 1/velocity in medium 2 is

Since frequency is the same in both media v is proportional to λ (v = fλ)

v_{1}/v_{2} = λ_{1}/λ_{2} = 2/1

This is a screenshot from Paul Falstad´s ripple tank simuator

In the blue area the water is

The wave travels slower in the blue area so the water is less deep.

This image is a screenshot from Paul Falstad´s ripple tank simulator

If the difference between distance XP and YP is 2 cm the wavelength is:

P is in the first minimum so path difference = λ/2

This image is a screenshot from Paul Falstad´s ripple tank simulator

If the difference between distance XP and YP is 2 cm the wavelength is:

P is in the first maximum so path difference = λ

This screenshot from Paul Falstad´s ripple tank shows waves diffracting through a single slit

The waves would definitely spread out more if:

reducing the slit width and increasing wavelength both result in a wider angle

This screenshot from Paul Falstad´s ripple tank shows waves diffracting through a single slit

If the slit width is reduced:

angle of diffraction increases and less wave passes through the slit so the amplitude is reduced

The diagram below shows a wave in a string incident on a narrow slit.

When the wave passes though the slit it will:

Only the component in the direction of the slit will pass through.

An unpolarised wave passes along a string. When it meets a vertical slit

I´m not sure what would actually happen but according to this simple model all components in line with the slit will pass.

When a guitar string is plucked, the wave

The wave isn´t normally polarised but can be if you restrict it lightly with your finger.

A standing wave is formed when the wave shown reflects off the fixed end.

The distance between nodes will be:

A standing wave can be formed in a string by vibrating each end. This causes waves to travel along the string in both directions, these waves add to give a standing wave.

To form a standing wave the sources do not have to be

changing the phase wil change the positions of the nodes but a standing wave can still be formed. In practice reflections will confuse the matter

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