Topic 4 Oscillations and Waves

4.4 Wave Properties

Reflection and Transmission

When a wave crosses a boundary between 2 media the wave will be partly reflected and partly transmitted.

The amount of reflection and transmission depends on the nature of the boundary.If the wave is able to move at the boundary then the reflected wave will be in phase. (A Soft Boundary)

If the wave is fixed at the boundary then the reflected wave will be out of phase. (A Hard Boundary)

Reflection and Transmission

As waves move from one medium into another the wave is partially transmitted and partially reflected.If the boundary is from low density to high density then this is a hard boundary and the reflected wave suffers a phase change.

If the boundary is from high density to low density then this is a soft boundary and the reflected wave is reflected in phase.

i

R

r

The Law of Reflection

The angle of incidence always equals the angle of reflection.

i

R

Changing Media

As waves move from one medium into another their wavespeed will change.

Transverse waves usually have more resistance to propagation in dense materials The wave will therefore usually travel slower in more dense materials.

The refractive index (1n2) is the ratio of the speeds to the wave in medium 2 to that in medium 1

The absolute refractive (n2) index is that when medium 1 is a vacuum, i.e. cn2.

Refractive Indices

The refractive indices of some common materials are shown below. Calculate the speed of light in these materials

Materialnv x108 ms-1

Air1.0003Water1.333Perspex1.49Crown Glass1.52Diamond2.42

Changing Media

When a wave crosses a boundary between two media at an angle other than the normal it will change direction.

This is called refraction

The amount of refraction is predicted by Snells law:

Refraction

When light crosses from a less optically dense medium into an more optically dense medium the light refracts towards the normal.

When light crosses from a more optically dense medium into an less optically dense medium the light refracts away the normal.

i

r

Refraction and Critical Angle

The use of a semi-circular block of medium allows the effect of moving from a high optical density to a low optical density to be studied.

Any ray that enters the block along a radius will strike the curved surface normally and hence will not refract.

As light exits a material into air or the vacuum it will refract away from the normal.

At some angle of incidence, the refracted ray will be directly along the flat surface of the block.

This is known as the critical angle c.

The refractive index of the medium can hence be determined.

c

Diffraction

When a plane wave encounters a gap in a barrier then the waves that pass through will become curved at the edges and spread out.

This is called diffraction.This is the phenomenon that allows sound to travel around corners

The amount of diffraction depends on the ratio of the width of the gap and the wavelength.

Diffraction

If the gap width (d) is much larger than the wavelength then the wave passes through with only small diffraction.

Diffraction

If the gap width (d) is larger than the wavelength then the wave passes through with only more diffraction.

The wave ends start to noticeable curve

Diffraction

If the gap width (d) is slightly wider than the wavelength then the wave passes through with a lot of diffraction.

The wave looks more curved than straight

Diffraction

If the gap width (d) is exactly the same width as the wavelength then the wave passes through and forms perfectly circular waves.

There are now no shadows

Examples of Diffraction

Water waves are often seen diffracting as they enter a harbour.

Sound can be heard around a corner due to diffraction

Examples of Diffraction

Light also diffracts but this is much less noticeable than sound because of the short wavelength of light.

Often the image suffers chromatic aberrationDifferent colours of light have different wavelengths so are diffracted by different amounts.

This colour splitting is known as dispersion

Superposition

Two waves that exist in the same space are able to propagate through each other.

When the two waves interact, the resultant wave form is that formed by the superposition of the two waves.

Superposition is the vector addition of the two amplitudes.

Superposition

If the two waves are in phase at the interaction, then the amplitude increases.This is constructive superposition.

If the two waves are out of phase at the interaction, then the amplitude is zero.This is destructive superposition.

Superposition and Harmonics

Musical Instruments rarely produce pure notes.

Usually additional harmonics are audiable.

If the fundamental frequency of a string instrument is f, then the harmonics are:2f, 3f, 4f etc.