WavesTopic 4.4 Wave characteristics

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.

Travelling Waves

There are two types of wave motion that we encounter in the physical world. Transverse Longitudinal

Transverse The source that produces the wave

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

Thus, 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 oscillation

of the particles

Transverse Wave

Longitudinal The source that produces the wave

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

Thus, 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 wave travels down it

This applies to longitudinal waves too

Wavefronts vs. Rays

• All the points of disturbance that originate from a source at the same time make up the wavefront– If the source was a single point, wavefronts will

be circular– If the source is a straight line, the wavefronts will

be parallel

• Rays are used to represent the direction of energy transfer

Wavefronts and rays

The wavefronts typically show where the crests of the waves are. The rays are always at 90 deg to the wavefronts.

rays

Wavefronts

Ray point of view Wave point of view

Light travels out instraight lines from asmall source

Light spreads out inspherical wavefrontsfrom a small source

Wavefronts in a parallelbeam or from a very distantsource are straight (notcurved) and parallel

Light in a parallel beam orfrom a very distant sourcehas rays (approximately)parallel to one another

Ray and wave points of view show the same thing butin different ways

Displacement

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

Amplitude

The maximum displacement of a particle from its equilibrium positionAlso equal to the maximum

displacement of the source that produces the wave).

Wavelength

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

wave energy in one period

Period (T) This is the time that it takes a

particle to make one complete oscillation

Also equals the time for the source of the wave to make one complete oscillation.

Also equals the time for the wave energy to travel a distance equal to the wavelength of the wave

Frequency

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

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

Wave Speed

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

Wave speed depends only on the nature and properties of the medium

Intensity

Since waves transfer energy, the rate of this transfer is described by power.

The amount of power per unit area is the intensity

Intensity diminishes further from a source as the wavefronts spread out

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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.

Transverse waves

Crests

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

Wavelength Again!!! The wavelength will be equal to the

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

Longitudinal waves

Compressions and rarefactions

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.

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

Interpreting Graphs of wave motion

Two types:

•Displacement vs. Distance

•Displacement vs. Time

Displacement / Distance

displacement

distance

Waves are periodic both in time and space. If we were to “freeze” time…

The y-axis shows the displacement of the wave medium from its equilibrium positionThe x-axis represents the distance the wave energy has traveled from some reference point, the location of the source, typically.

displacement

distance

amplitudewavelength

amplitude

wavelength

Note: there is no period information here!

Displacement / Distance

Displacement / Distance

displacement

distance

Now lets consider a single position on the wave labeled P…

P

If we were to “unfreeze” time and analyze how the displacement of P varies in time, the resulting diagram would look like…

Displacement / Time

displacement

time

•The y-axis represents the displacement of point P from equillibrium•The x-axis represents the passage of time

Displacement / Time

displacement

time

amplitudeperiod

period

Note: there is no wavelength information here