Equations

v = λf

Frequency in hertz (Hz)

f = 1 / t

wave speed = wave length * frequency

n = sin( i ) / sin( r )

sin( c ) = 1 / n

Transverse / Longitudinal Waves

• Waves can exist as one of two types:

• Transverse

• Longitudinal

Transverse Waves

• Transverse waves are defined as:

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

The electromagnetic spectrum is composed of transverse waves

Transverse waves do not need a medium to travel

Longitudinal Waves

• Longitudinal waves are defined as:

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

Longitudinal Waves need a medium to travel through

Properties of both wave types

Describing Wave Motion

Amplitude

• Amplitude is defined as:

The distance from the undisturbed position to the peak or trough of a wave

• It is given the symbol A and is measured in metres (m)

• Amplitude is the maximum or minimum displacement from the undisturbed position

Wavelength

• Wavelength is defined as

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

• In a transverse wave:

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

• In a longitudinal wave

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

• 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

Diagram showing the amplitude and wavelength of a wave

Frequency

• Frequency is defined as:

The number of waves passing a point in a second

• Frequency is given the symbol f and is measured in Hertz (Hz)

Time Period

• 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 time period is given the symbol T and is measured in seconds (s)

Wavefront

• Wavefronts are a useful way of picturing waves from above: each wavefront is used to represent a single wave

• The image below illustrates how wavefronts are visualised:

  • The arrow shows the direction the wave is moving and is sometimes called a ray

  • The space between each wavefront represents the wavelength

  • When the wavefronts are close together, this represents a wave with a short wavelength

  • When the wavefronts are far apart, this represents a wave with a long wavelength

Diagram showing a wave moving to the right, drawn as a series of wavefronts\

The Doppler Effect

• The Doppler Effect is defined as:

The apparent change in wavelength and frequency of a wave emitted by a moving source

• The wavefronts are closer together

• The wavelength is shorter, therefore the frequency is higher ( they are inversely proportional)

• Wave speed is the same

• This is the doppler effect

Applications of EM Waves

Dangers of EM Waves

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

• Reflection occurs when:

Reflection and Refraction

F aster
A way

S lower

T owards

Reflection occurs when

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

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

Waves can change direction when moving between materials with different densities

The Law of Reflection

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

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

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

• The angles are the same, so the law of reflection can be written:

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

Angle of incidence and angle of reflection

Ray Diagrams

Reflection Ray Diagrams

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

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

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

• The law of reflection states that these angles are the same

Ray diagram of reflection of a wave at a mirror

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

  • An incident ray has an arrow pointing towards the boundary

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

• The angles of incidence and reflection are usually labelled i and r respectively and measured from the normal

Total Internal Reflection

• Sometimes, when light is moving from a denser medium towards a less dense one, instead of being refracted, all of the light is reflected

  • This phenomenon is called total internal reflection

• Total internal reflection (TIR) occurs when:

The angle of incidence is greater than the critical angle and the incident material is denser than the second material

• Therefore, the two conditions for total internal reflection are:

  • The angle of incidence > the critical angle

  • The incident material is denser than the second material

Critical angle and total internal reflection

• Total internal reflection is utilised in:

  • Optical fibres eg. endoscopes

  • Prisms eg. periscopes

Oscilloscopes

• An oscilloscope is a device that can be used to study a rapidly changing signal, such as:

  • A sound wave

  • An alternating current

Oscilloscopes have lots of dials and buttons, but their main purpose is to display and measure changing signals like sound waves and alternating current

• When a microphone is connected to an oscilloscope, the (longitudinal) sound wave is displayed as though it were a transverse wave on the screen

• The time base (like the 'x-axis') is used to measure the time period of the wave

A sound wave is displayed as though it were a transverse wave on the screen of the oscilloscope. The time base can be used to measure a full time period of the wave cycle

• The height of the wave (measured from the centre of the screen) is related to the amplitude of the sound

• The number of entire waves that appear on the screen is related to the frequency of the wave

  • If the frequency of the sound wave increases, more waves are displayed on screen

Measure the speed of sound

Use a signal generator with a loudspeaker to produce a sound with a constant frequency

Attach two microphones to a dual channel oscilloscope

Start with the microphones together and move them until the waves are lined up on the screen.

Distance between the microphones is the wavelength

Use f = 1 / t and the oscilloscope to find the frequency

Use v = wl * f to find the speed of sound