Waves

Transverse & longitudinal waves

• Waves can come in one of two types:

o Transverse waves

o Longitudinal waves

Transverse waves

• Transverse waves are defined as:

Waves that vibrate or oscillate perpendicular to the direction of energy transfer

• Transverse waves:

o oscillate perpendicularly to the direction of travel

o transfer energy, but not the particles of the medium

o exist as mechanical waves which can travel in solids and on the surfaces of
liquids but not through liquids or gases

o exist as electromagnetic waves which can move in solids, liquids, gases and in a vacuum

• On a transverse wave:

o the highest point above the rest position is called a peak, or crest

o the lowest point below the rest position is called a trough

Example of a transverse wave

Transverse waves can be seen in a rope when it is moved quickly up and down

• Examples of transverse waves are:

o Ripples on the surface of water

o Vibrations in a guitar string

o S-waves (a type of seismic wave)

o Electromagnetic waves (such as radio, light, X-rays etc)

Longitudinal waves

• Longitudinal waves are defined as:

Waves where the points along its length vibrate parallel to the direction of energy transfer

• Longitudinal waves:

o Oscillate in the same direction as the direction of wave travel

o Transfer energy, but not the particles of the medium

o Move in solids, liquids and gases

o Cannot move in a vacuum (since there are no particles)

• The key features of a longitudinal wave are where the points are:

o Close together, called compressions

o Spaced apart, called rarefactions

Example of a longitudinal wave

Longitudinal waves can be seen in a slinky spring when it is moved quickly backwards and forwards

• Examples of longitudinal waves are:

o Sound waves

o P-waves (a type of seismic wave)

o Pressure waves caused by repeated movements in a liquid or gas

Comparing transverse & longitudinal waves
• Wave vibrations can be shown on ropes (transverse) and springs (longitudinal)

A comparison of longitudinal and transverse waves

Waves can be shown through vibrations in ropes or springs

Properties of transverse and longitudinal waves

Property Transverse Waves Longitudinal Waves

Structure Peaks and troughs Compressions and rarefactions
Vibration Perpendicular to the direction of energy transfer Parallel to the direction of energy transfer
Vacuum Can travel in a vacuum (electromagnetic waves) Cannot travel in a vacuum
Material Can travel through solids, and on the surface of Can travel through solids, liquids and gases
liquids
Density Constant density Changes in density
Pressure Pressure is constant Changes in pressure
Speed of Dependent on material it is travelling through Dependent on material it is travelling through
wave (fastest in a vacuum) (fastest in a solid)

Worked Example

The diagram below shows a loudspeaker generating sound waves, which travel to the right as indicated.
Sound waves are longitudinal. A dust mote floats in the air just next to the loudspeaker, labelled D. Draw
arrows on the diagram to indicate how the dust mote D would vibrate as sound waves pass it.

Answer:

Step 1: Recall the definition of longitudinal waves

• Points along longitudinal waves vibrate parallel to the direction of energy transfer

• This means the dust mote vibrates in a line parallel to the direction of the sound waves drawn

Step 2: Draw arrows at the point labelled D to show it vibrating in parallel to the direction of the
sound waves
Waves & energy

• Waves are disturbances caused by an oscillating source that

transfer energy and information without transferring matter

• Waves are described as oscillations or vibrations about a fixed point

o For example, ripples cause particles of water to oscillate up and down

o Sound waves cause particles of air to vibrate back and forth

Evidence that waves transfer energy and not matter

Waves transfer energy and information, but not matter. This toy duck bobs up and down as water
waves pass underneath

• The wave on the surface of a body of water is a transverse wave

• The duck moves perpendicular to the direction of the wave

o The duck moves up and down but does not travel with the wave
Describing wave motion
• When describing wave motion, there are several terms which are important to know, including:

o Amplitude (A)

o Wavelength (λ)

o Frequency (f)

o Time Period (T)

Amplitude (A)

• Amplitude is defined as:

Amplitude is the maximum or minimum displacement from the undisturbed position

• The maximum displacement of a wave is the peak

• The minimum displacement of a wave is the trough

• Amplitude is measured in metres (m)

Wavelength (λ)

• Wavelength is defined as

The distance from one point on the wave to the same point on the next wave

• In a transverse wave:

o The wavelength can be measured from one peak to the next peak

• In a longitudinal wave:

o The wavelength can be measured from the centre of one compression to the centre of
the next

• Wavelength is measured in metres (m)

Graphical representation of transverse waves
• The amplitude and wavelength of a transverse wave can be represented graphically

• The distance along a wave is typically put on the x-axis of a wave diagram

A diagram of a transverse wave

Diagram showing the amplitude and wavelength of a transverse wave

• The wavelength is given the symbol λ (lambda) and is measured in metres (m)

• The distance along a wave is typically put on the x-axis of a wave diagram

Frequency (f)

• Frequency is defined as:

The number of waves passing a point in a second

• Frequency is measured in hertz (Hz)

o The unit hertz is equivalent to 'per second'

o 5 Hz = 5 waves per second

• Waves with a higher frequency transfer a higher amount of energy

Time Period (T)

• The time period (or sometimes just 'period') of a wave is defined as:

The time taken for a single wave to pass a point

• The period is measured in seconds (s)

• The equation linking frequency and time period is explained in Frequency & time period
Examiner Tips and Tricks

In your exam, you are expected to be able to define these keywords and identify their values from
diagrams or scenarios.

The wavelength is often shown graphically between the peaks of two consecutive waves. However, the
wavelength can be shown between two corresponding points on two successive waves - the distance will
be the same!

The wave equation

• All waves obey the wave speed equation

o This is the relationship between the wave speed, frequency and wavelength of a wave

• Where:

o v = wave speed in metres per second (m/s)

o f = frequency in hertz (Hz)

o λ = wavelength in metres (m)

Formula triangle for the wave speed equation

A formula triangle can be used to help rearrange the wave speed equation

• For more information on how to use a formula triangle refer to the revision note on Speed
Frequency & time period

• Frequency and time period are defined in Describing wave motion

• The following equation relates time period and frequency:

• Where:

o f is frequency measured in Hertz (Hz)

o T is time period, measured in seconds (s)

Worked Example

Visible light has a frequency of about 6 × 1014 Hz.

How long does it take for one complete cycle of visible light to enter our eyes?

A certain sound wave moves at about 330 m/s and has a time period of 0.0001 seconds.

Calculate:

a) The frequency of the sound wave

b) The wavelength of the sound wave

A local radio station broadcasts at a frequency of 200 kHz. The wavelength of these radio waves is 1500
m.

Calculate the speed of these radio waves and state an appropriate unit.

Properties of EM waves
• Light is part of a continuous electromagnetic spectrum that consists of the following types of
radiation:

o radio

o microwave

o infrared

o visible

o ultraviolet

o x-ray
 o gamma ray

• All waves in the electromagnetic spectrum share the following properties:

o They are all transverse

o They can all travel through free space (a vacuum)

o They all travel at the same speed in free space

The EM spectrum
• The types of radiation found in the electromagnetic spectrum have a specific order based on
their wavelength (and frequency)

• This order listed above has:

o Radio waves at the top because they have the longest wavelength (and lowest
frequency)

o Gamma rays at the bottom because they have the shortest wavelength (and highest
frequency)

• Wavelength and frequency are inversely proportional to each other:

o An increase in wavelength is a decrease in frequency (towards the red end of the

spectrum)

o A decrease in wavelength is an increase in frequency (towards the violet end of the

spectrum)

o This is explained by the Wave equation

The types of radiation in the EM spectrum from longest to shortest wavelength

Visible light is just one small part of a much bigger spectrum: The electromagnetic spectrum

Visible Spectrum
• Visible light is the only part of the EM spectrum detectable by the human eye

o However, it is only a very small part of the whole electromagnetic spectrum

o In the natural world, many animals, such as birds, bees and certain fish, can perceive
beyond visible light and use infra-red and UV wavelengths of light to see

• Each colour within the visible light spectrum corresponds to a narrow band
of wavelength and frequency

• The different colours of waves correspond to different wavelengths:

o Red has the longest wavelength (and the lowest frequency)

o Violet has the shortest wavelength (and the highest frequency)

The colours of the visible spectrum

The colours of the visible spectrum: red has the longest wavelength; violet has the shortest

Examiner Tips and Tricks

See if you can make up a mnemonic to help you remember the order of the colours of visible light in the
EM spectrum!.

One possibility is:

Raging Martians Invaded Venus Using X-ray Guns

To remember the colours of the visible spectrum you could remember either:

• The name “Roy G. Biv”

• Or the saying “Richard Of York Gave Battle In Vain”

You could even combine both to have a mega mnemonic:

Raging Martians Invaded Roy G. Biv Using X-ray Guns!

The electromagnetic spectrum is usually given in order of decreasing wavelength and increasing
frequency i.e. from radio waves to gamma waves

Remember:

• Radios are big (long wavelength)

• Gamma rays are emitted from atoms which are very small (short wavelength)

Applications of EM waves
• Each region of the electromagnetic spectrum has a variety of uses and applications

Uses of EM waves
Wave Type Uses

Radio Broadcasting and communications

Microwaves Cooking and satellite transmissions

Infrared Heaters and night vision equipment

Visible light Optical fibres and photography

Ultraviolet Fluorescent lamps

X-rays Observing the internal structure of objects and materials, including

medical applications

Gamma Sterilising food and medical equipment

rays
Radio waves & microwaves

• Both radio waves and microwaves are used in wireless communication

• This includes:

o Radios

o Air traffic communication

o Mobile phone communication

• At very high intensities microwaves are used to heat things in a microwave oven

Infrared

• Infrared is emitted by warm objects and can be detected using special cameras (thermal imaging
cameras).

• Examples of the uses of infrared are:

o Security cameras to see people in the dark

o TV remote controls

o Transport signals down fibre optic cables

Visible

• Visible light is the only part of the electromagnetic spectrum that the human eye can see

• It is also used in fibre optic communication

Ultraviolet

• Ultraviolet is responsible for giving you a sun tan, which is your body’s way of protecting itself
against the ultraviolet

• When certain substances are exposed to ultraviolet, they absorb it and re-emit it as visible light
(making them glow)

o This process is known as fluorescence

• Fluorescence can be used to secretly mark things in special ink, such as banknotes

X-rays

• The most obvious use of x-rays is in medicine

• X-rays can pass through most body tissues but are absorbed by the denser parts of the body,
such as bones

Gamma Rays

• Gamma rays are dangerous and can be used to kill cells and living tissue
 • Gamma rays can also be used to sterilise equipment by killing off the bacteria

Dangers of EM waves

Risks of excessive exposure to EM radiation

• Excessive exposure of the human body to electromagnetic waves can have detrimental effects

• Risks from overexposure to certain wavelengths include:

o microwaves can cause heat damage to internal organs due to the internal heating of
body tissue

o infrared can burn the skin

o ultraviolet can damage skin cells causing sunburn and blindness

o gamma and X-rays can kill cells causing cancer and cell mutations

Dangers and uses of each part of the EM spectrum

Uses and dangers of the electromagnetic spectrum
 • As discussed in Describing wave motion as the frequency of electromagnetic (EM)
waves increases, so does the energy

• Beyond the visible part of the EM spectrum, the energy becomes large enough to ionise atoms

• As a result of this, the danger associated with EM waves increases along with the frequency

o The shorter the wavelength, the more ionising the radiation

Protective measures against the risks of over-exposure

• Devices using hazardous EM radiation contain safety features that reduce human exposure:

o microwaves from microwave ovens are prevented from escaping the oven by the metal
walls and metal grid in the glass door

o infrared wearing protective clothing such as gloves can prevent the skin from feeling the
hear

o ultraviolet ray damage to the eyes is reduced by wearing sunglasses that absorb
ultraviolet and prevent it from reaching the eyes. Sunscreen also absorbs ultraviolet light
preventing it from damaging the skin.

o gamma and X-rays damage is reduced through using minimal levels in medicine. Doctors
leave the room during x-rays to avoid unnecessary exposure. Radiographers wear
radiation badges to measure their level of radiation exposure. People working with
gamma rays routinely have their dose levels tested.

Radiation badges

Radiation badges are used by people working closely with radiation to monitor exposure

Light
 • Visible light is a part of the Electromagnetic spectrum which means it is a transverse wave

Representing a transverse wave

Light waves are transverse: the particles vibrate in a perpendicular direction to the energy transfer

• Light can undergo:

o Reflection

o Refraction

Sound
• Sound waves are longitudinal waves

• Longitudinal waves are usually drawn as several lines to show that the wave is moving parallel to
the direction of energy transfer

o Drawing the lines closer together represents the compressions

o Drawing the lines further apart represents the rarefactions

Representing a longitudinal wave

Longitudinal waves are represented as sets of lines with rarefactions and compressions

• Sound can also undergo:

o Reflection

o Refraction

• The reflection of a sound wave is called an echo

Reflection & refraction

• All waves, whether transverse or longitudinal, can be reflected and refracted

• Reflection occurs when:

A wave hits a boundary between two media and does not pass through, but instead stays in the
original medium

• In optics the word medium is used to describe a material that transmits light

o Media means more than one medium

An example of reflection
An identical image of the tree is seen in the water due to reflection

• Refraction occurs when:

A wave passes a boundary between two different transparent media and undergoes a change in
direction

An example of refraction

Waves can change direction when moving between materials with different densities

The law of reflection

 • The law of reflection states that:

Angle of incidence (i) = Angle of reflection (r)

• Angles are measured between the wave direction (ray) and a line at 90 degrees to the boundary
called the normal

o The angle of the wave approaching the boundary is called the angle of incidence (i)

o The angle of the wave leaving the boundary is called the angle of reflection (r)

An example of reflection in a plane mirror

Ray diagram of the reflection of a wave in a mirror

Ray diagrams
Reflection ray diagrams
• When drawing a ray diagram an arrow is used to show the direction the wave is travelling

o An incident ray has an arrow pointing towards the boundary

o A reflected ray has an arrow pointing away from the boundary

A diagram showing the law of reflection

The angle of incidence and angle of reflection are equal in the law of reflection

Refraction ray diagrams

• The direction of the incident and refracted rays are also taken from the normal line

• The change in direction of the refracted ray depends on the difference in density between the
two media:

o From less dense to more dense (e.g air to glass), light bends towards the normal

o From more dense to less dense (e.g. glass to air), light bends away from the normal

o When passing along the normal (perpendicular) the light does not bend at all
A diagram of a ray refracted into and out of a glass block

How to construct a ray diagram showing the refraction of light as it passes through a rectangular
block

• The change in direction occurs due to the change in speed when travelling in different
substances

o When light passes into a denser substance the rays will slow down, hence they bend
towards the normal

• The only properties that change during refraction are speed and wavelength – the frequency of
waves does not change

o Different frequencies account for different colours of light (red has a low frequency,
whilst blue has a high frequency)

o When light refracts, it does not change colour (think of a pencil in a glass of water),
therefore, the frequency does not change