Oscillations & Waves, Reflection & Refraction

• A progressive wave or travelling wave consists of a vibration carrying energy from a source to the surroundings
In the above, the source of the wave is the vibrating stick. The wave moves away from the stick. The cork is initially at rest, but when the wave arrives, it starts to move up and down. This means that the cork has been given energy (kinetic), carried to it from the stick by the wave. However, note that matter has not moved from the wave source to the cork, just the vibration.

Types of progressive waves

a) Transverse waves

• In a transverse wave, the vibrations are at right angles to the direction the wave travels
We can produce transverse waves on a rope by shaking the end up and down:
The transverse wave produced appears as a sequence of alternate crests and troughs moving in the direction of the wave.
• Light waves are transverse (we cannot see the waves, but there is indirect evidence for this - see later)
• Water waves look transverse (though the motion of individual particles is somewhat side to side, as well as up and down)
b) Longitudinal waves
• In a longitudinal wave the vibrations are along the same direction as the wave moves
The hand vibration is parallel to the length of the spring.

The longitudinal wave produced appears as a sequence of alternate of compressions (where links are closer together than normal) and rarefactions (where links are further apart than normal) moving in the direction of the wave.

• Sound waves are longitudinal
We can understand why this is if we consider the sound wave produced by a tuning fork:
Light and sound
• Light can travel though a vacuum. Light travels through 150 million km (93 million miles) of (almost) empty space in reaching the earth from the sun
• Sound cannot travel though a vacuum. Sound is made up of the vibrations of atoms or molecules passing through a substance, and so without atoms or molecules (i.e. in a vacuum) it cannot travel
Mechanical and electromagnetic waves

All waves are in one of these groups

• Mechanical waves are produced by vibrations in a material medium. E.g. Waves on a rope (transverse); sound waves (longitudinal).
• Electromagnetic (‘em’) waves consist of vibrations in the form of varying electric and magnetic fields. They include radio waves, light, x-rays …(see later). EM waves require no material medium in order to travel, i.e. they can all pass though a vacuum. However, some can also pass through matter - for example, light passes through water and glass and x-rays pass through flesh. All em waves are transverse.

Amplitude and wavelength

• The amplitude is the maximum displacement of each vibrating point from its equilibrium position
• The wavelength is the distance between any two successive corresponding points. This could be between successive crests in a transverse wave, as shown above, or between successive compressions in a longitudinal wave
Frequency

The frequency of something is how many times it happens per second (or per minute or per year etc.). For a tuning fork, its frequency is the number of vibrations its prongs perform each second.

• The frequency of a wave is the number of wavelengths to pass a given point in on second
We’ve considered a wave produced by shaking a rope up and down or a slinky spring side to side. Each complete cycle of vibration produces one complete wave.

Speed

The speed of a wave is the distance moved by a fixed point on the wave per second. This implies:

Note: Taking light as an example, when it passes from, say, air to glass, its wavelength and speed both change, but its frequency does not. So frequency may be considered to be a more fundamental quantity than wavelength for a wave.

Example

The typical range of sound frequencies a person can hear is from about 20Hz to 20kHz. Calculate the corresponding range of wavelengths. (speed of sound = 340m/s)

Transverse waves on a string can be produced by fixing one end and shaking the other end in any direction perpendicular to the string.

If one particular direction is used, the vibrations of the string will be in one plane, and the wave is said to be plane-polarised. For example, up and down vibrations produce a vertically polarised wave.

In the set up below, the end of the string is shaken in all directions at 900 to the string to produce unpolarised transverse waves passing along the string. The first slit, S1, only allows vibrations in the vertical plane to pass. Thus, the unpolarised wave emerges from S1 polarised in the vertical plane.

If the slits are parallel, i.e. S2 is also vertical, then the polarised waves passes through S2:

If the slits are ‘crossed’, i.e. S2 is horizontal, i.e. at 900 to S1, then the wave is stopped:

• Polarisation is a characteristic of transverse waves and not longitudinal waves - electromagnetic waves (which includes visible light) can be polarised, but sound waves cannot
Polarisation of light

When a lamp is viewed through a single Polaroid, which is rotated, no variation in intensity is observed. However, when a lamp is viewed through two Polaroids and one is rotated, the light intensity varies from a maximum to darkness.

To explain this we infer:
1. Light is a transverse wave motion
2. Light from the lamp is unpolarised
3. A Polaroid only lets vibrations in one direction pass through it, i.e. it polarises the light
4. Light only passes through both Polaroids when they are ‘parallel’ and not when they are ‘crossed’.

As the right hand Polaroid is rotated, a fraction of light passes though, the amount depending upon the angle of rotation.

Not only visible light, but all electromagnetic radiation can be polarised, which is taken as evidence that all electromagnetic radiation is a transverse wave motion.

Electromagnetic spectrum

This is a family of waves which we group into bands. There is no absolute sharp cut-off from one band to another.

The diagram indicates approximate wavelengths. Notice that visible light is a relatively small band of wavelengths in the overall spectrum.

• Radio waves are used to transmit radio and TV signals, and nowadays they are transmitted all around the world via satellites (radiowaves are also informally called 'airwaves')
• Infrared rays are felt as warmth on the skin
• The visible band is made up of the spectrum of rainbow colours:
• Ultraviolet rays can produce a suntan - and be harmful if the skin is overexposed
• X-rays can penetrate solid objects and affect a film – useful for taking ‘pictures’ of bones
• Gamma rays are emitted by radioactive sources. They are more penetrating and dangerous than x-rays. They have beneficial uses, such as, for example, for treating cancer

Unlike transverse waves on a string, say, there are no particle vibrating in an electromagnetic wave. So what is vibrating? It is believed that all em waves can be regarded as being composed of a varying electric field coupled with a varying magnetic field. These fields are at 900 to each other and both at 900 to the direction of travel. The vibrations of both fields are transverse.

We call the set of electromagnetic waves a ‘family’ because they share common features. They all:

• have the same basic character (described above)
• are transverse (evidence from polarisation)
• can travel through a vacuum (also called ‘free space’)
• travel at the speed of light (denoted by ‘c’, and equal to 3x108m/s)
• obey the wave equation: c = frequency * wavelength
Example
BBC radio 2 broadcasts on 1.5km. What is its frequency? (c = 3 * 108m/s)

Note: Though a radio emits audible sound, which travels at the speed of sound in air, the signal arriving at the radio was transmitted as a radio wave, so in the above calculation we use the speed of light, which is the speed of all electromagnetic waves in vacuum.

The following represents a top view of a ripple tank:

The lines moving away from the dippers represent ‘wavefronts’. All points on a wavefront are in step or 'in phase' with each other. Thus, the wavefronts indicated above may be lines passing through crests (or troughs) of the water waves, and so the distance between the lines represents the wavelength of the waves.

A ray is a line drawn at right angles to a wavefront indicating the direction of travel.

Reflection

• Diffraction is the bending of waves as they pass through a gap or past an edge
A barrier with a gap can be placed in the water in a ripple tank.

a) Gap much greater than wavelength

If the gap is wide the waves pass though almost unaffected, i.e. very little diffraction:

b) Gap about equal to wavelength

If the gap is narrow, the wavefronts bend a great deal.

• Maximum diffraction occurs when the gap is about equal to the wavelength of the waves
Diffraction is a characteristic of wave motions. Light waves diffract when they pass though a sufficiently small gap (recall that the wavelength of light is about 10-7m) . Sound waves will bend round doors (they have a much longer wavelength than light waves).

A Level Physics - Copyright © A C Haynes 1999 & 2004