WavesTopic 4.4 Wave characteristics

Travelling Waves

There are two types of waves and pulses that we encounter in the

physical world.

Transverse In these waves the source that

produces the wave oscillates at right angles to the direction of travel of the wave

It means that the particles of the medium through which the wave travels also oscillates at right angle to the direction of travel of the wave.

Direction of travelof the wave

Direction of oscillationof the particles

Transverse Wave

Longitudinal In these waves the source that

produces the wave oscillates in the same direction as the direction of travel of the wave

It means that the particle of the medium through which the wave travels also oscillates in the same direction as the direction of travel of the wave.

Longitudinal Wave

Direction of travelof the wave

Direction of oscillationsof the particles

Discrete Pulses and Continuous Waves

A single shake of a slinky will send a discrete pulse down it

Shake the slinky up and down and a continuous travelling wave travels down it

This applies to longitudinal waves too

What is a Wave?

A wave is a means by which energy is transferred between two points in a medium without any net transfer of the medium itself.

The Medium

The substance or object in which the wave is travelling.

When a wave travels in a medium parts of the medium do not end up at different places

The energy of the source of the wave is carried to different parts of the medium by the wave.

Water waves however, can be a bit disconcerting.

Waves at sea do not transport water but the tides do.

Similarly, a wave on a lake does not transport water but water can actually be blown along by the wind.

However, if you set up a ripple tank you will see that water is not transported by the wave set up by the vibrating dipper.

A very important property associated with all waves is their so-called periodicity.

Waves in fact are periodic both in time and space and this sometimes makes it difficult to appreciate what actually is going on in wave motion.

Periodicity

If we drew a diagram that froze time on waves in water

an instantaneous snapshot of the whole of the water surface

The next diagram shows the periodicity of the wave in space

Displacement / Distance

displacement

distancep

The y-axis shows the displacement of the water from its equilibrium position

The graph is a displacement-distance graph.

We now look at one part of the wave that is labeled p and "unfreeze" time

The next diagram shows how the position of p varies with time

This illustrates the periodicity of the wave in time

Displacement / Time

displacement of point p from equilibrium position

time

The y-axis now shows the displacement of the point p from equilibrium

The graph is a displacement-time graph.

The space diagram and the time diagram are both identical in shape

If we mentally combine them we have the whole wave moving both in space and time.

And for Longitudinal Waves?

For the longitudinal wave in the slinky spring the displacement-distance graph actually shows the displacement of the individual turns of the spring from their equilibrium position as a function of distance along the spring.

However

It could equally show how the density of turns of the spring varies with length along the spring.

The displacement-time graph shows the displacement of one turn of the spring from its equilibrium positions as a function of time.

Definitions

The following definitions are given in terms of the particles that make up the medium through which the wave travels.

For the slinky spring a particle would be a single turn of the spring

For the water waves a particle would be a very small part of the water.

Wavefront

• All the points that started from a source at one time make up the whole of that wavefront,

• If it was a single point, it will be a circular wavefront

• If it is a straight line, it will be a straight wave front

Displacement

(s) is the distance that any particle is away from its equilibrium position at an instance

Measured in metres

Amplitude

(A, a) This is the maximum displacement of a particle from its equilibrium position

(It is also equal to the maximum displacement of the source that produces the wave).

Normally measured in metres

Period

(T) This is the time that it takes a particle to make one complete oscillation

(It also equals the time for the source of the wave to make one complete oscillation).

Measured in seconds

Frequency

(f) This is the number of oscillations made per second by a particle

(It is also equal to the number of oscillations made per second by the source of the wave)

The SI unit of frequency is the hertz -Hz. (1 Hz is 1 oscillation per second)

Clearly then, f = 1/T

Wavelength

() This is the distance along the medium between two successive particles that have the same displacement and the same phase of motion.

Measured in metres

Wave Speed

(v, c) This is the speed with which energy is carried in the medium by the wave.

Measured in ms-1

A very important fact is that wave speed depends only on the nature and properties of the medium

Crest

This is a term coined from water waves and refers to the points at the maximum height of the wave.

Trough

A term coined from water waves referring to the points at the lowest part of the wave.

Wavelength again!

Wavelength will therefore be equal to the distance between successive crests and successive troughs.

Compression

This is a term used in connection with longitudinal wave and refers to the region where the particles of the medium are "bunched up".

High density High pressure

Rarefaction

A term used in connection with longitudinal waves referring to the regions where the particles are "stretched out".

Low density Low pressure

Longitudinal Waves The wavelength will be equal to the

distance between successive points of maximum compression and successive points of maximum rarefaction.

The compression is the region in which the molecules of the air are pushed together

The rarefaction is the region where the molecules move apart.

rarefactions

wavelength

Sound Waves

A longitudinal wave in a slinky spring is analogous to a sound wave in which each turn of the spring represents an air molecule.

Interpreting Graphs - 1

displacement

distance

crest

trough

amplitude crestwavelength

amplitude

wavelength

Interpreting Graphs - 2

displacement

time

amplitudeperiod

period

Deriving v = f Imagine a wave with velocity v Being produced from a source of

frequency f In 1 second the 1st wavefront would

have travelled a distance of f As speed = distance / time v = f / 1 v = f

2 Important Points

1. The frequency of a wave depends only on the source producing the wave

It will therefore not change if the wave enters a different medium or the properties of the medium change

2. The Speed of waves only depends on the nature and the properties of the medium

Water waves do travel faster in deeper water

Light travels slower in more optically dense material

The EM Spectrum Itself

Short Long High fLow f

VISIBLERadioWaves

MicroWaves

Infrared

Gammarays

UltraViolet

Xrays

Frequencies of Regions (Hz)

• Gamma Rays >1021

• X-rays 1017- 1021

• Ultraviolet 1014 - 1017

• Violet 7.5 x 1014 > Visible > Red 4.3 x 1014

• Infrared 1011 -1014

• Microwaves 109 -1011

• Radio and TV < 109

The Different Regions In the context of wave motion, common

properties of all parts of the electromagnetic spectrum are

all transverse waves all travel at the speed of light in vacuo

(3.0 x 108 ms-1) all can travel in a vacuum

Sources of Regions Gamma – certain radioactive material’s nuclei X-rays – by firing an electron stream at a tungsten

metal target in a highly evacuated tube. Ultraviolet – the Sun, ultraviolet lamp Visible – hot bodies Infrared – the Sun (heat), hot bodies Microwaves – Ovens, communication systems Radio and TV – transmitter stations, Azteca TV