Oscillations & Waves, Reflection & Refraction

WAVES (Part 1) (return to CONTENTS)


PROGRESSIVE WAVES (return to start of page)

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

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.   b) Longitudinal waves
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.

We can understand why this is if we consider the sound wave produced by a tuning fork:
Light and sound Mechanical and electromagnetic waves

All waves are in one of these groups


THE WAVE EQUATION (return to start of page)

Amplitude and wavelength

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.

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)


POLARISATION (return to start of page)

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 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 WAVES (return to start of page)

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.

Character of electromagnetic radiation

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.

Common features of em radiation

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

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.


WAVEFRONTS AND RAYS (return to start of page)

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 (return to start of page) 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.

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).

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