Unit 3 Waves

What is a progressive wave?

A wave that transfers energy without transferring material and is made up of particles oscillating

What is amplitude?

A wave’s maximum displacement from the equilibrium position

What is frequency?

The number of completer oscillations passing through a point per second

What is wavelength?

The length of one whole oscillation

What is speed?

Distance travelled per unit time

What is phase?

The position of a certain point on a wave cycle

What is phase difference?

How much a particle/wave lags behind another particle/wave

What is the period?

Time taken for one full oscillation

When are 2 points on a wave said to be in phase?

When they are both at the same point of the wave cycle this means they will have the same displacement and velocity and their phase difference will be a multiple of 2π. They will have the same frequency and wavelength

When are 2 points said to be completely out of phase?

When they’re an odd integer of half cycles apart

What is the equation for the speed of a wave?

speed = frequency times wavelength

What is the equation for frequency in terms of period?

frequency = 1/period

What are transverse waves?

When the oscillation of particles is at right angles to the direction of energy transfer

What type of wave are electromagnetic waves?

Transverse

What are longitudinal waves?

The oscillation of particles which is parallel to the direction of energy transfer. They are made up of compressions and rarefactions and can’t travel in a vacuum

What is a polarised wave?

A wave that only oscillates in one plane

What does polarisation provide evidence for?

The nature of transverse waves because polarisation can only occur if a wave’s oscillations are perpendicular to its direction of travel

What are the applications of polarisation?

Polaroid sunglasses reduce glare by blocking partially polarised light reflected from water and tarmac making it easier to see.

TV and radio signals are usually plane polarised by the orientation of the rods on the transmitting aerial so the receiving aerial must be aligned in the same plane of polarisation to receive the signal at full strength

What is superposition?

Where the displacements of 2 waves are combined as they pass each other the resultant displacement is the vector sum of each wave’s displacement

What is constructive interference?

When 2 waves have displacement in the same direction

What is destructive interference?

When one wave has positive displacement and the other has negative displacement. If the waves have equal but opposite displacements, total destructive interference occurs

What is a stationary wave?

A wave that is formed from the superposition of 2 progressive waves, travelling in opposite directions in the same plane with the same frequency, wavelength and amplitude. It transfers no energy

What happens in a stationary wave?

Where the waves meet in phase, constructive interference occurs so antinodes are formed which are regions of maximum amplitude. Where the waves meet completely out of phase, destructive interference occurs and nodes are formed which are regions of no displacement

What is the first harmonic?

The lowest frequency at which a stationary wave forms with 2 nodes and a single antinode

What is the equation for the frequency of the first harmonic?

(1/(2*length of vibrating string))*(tension*mass per unit length)^0.5

How can the frequency for the nth harmonic be calculated?

By multiplying the first harmonic frequency by n

What are examples of stationary waves?

Stationary microwaves can be formed by reflecting a microwave beam at a metal plate, to find the nodes and antinodes use a microwave probe.

Stationary sound waves can be formed by placing a speaker at one end of a closed glass tube, lay powder across the bottom of the tube, it will be shaken at the antinodes and settle at the nodes. The distance between each node is half a wavelength, and the frequency of the signal generator to the speaker is known so by c=fλ the speed of sound in air can be found.

What is a coherent light source?

A light source that has the same frequency and wavelength and a fixed phase difference

What is an example of coherent and monochromatic light source?

Lasers emit a single wavelength of light and are usually used as sources of light in diffraction experiments as they form clear interference patterns

What is Young’s double slit experiment?

Shine a coherent light source through a double slit about the same size as the wavelength of the laser light so the light diffracts. Each slit acts as a coherent point source making a pattern of light and dark fringes.

How do interference patterns occur?

Each slit acts as a coherent point source making a pattern of light and dark fringes. Light fringes are formed where the light meets in phase and interferes constructively, this occurs where the path difference between waves is a whole number of wavelengths (nλ, where n is an integer). Dark fringes are formed where the light meets completely out of phase and interferes destructively, this occurs where the path difference is a whole number and a half wavelengths ((n+½)λ).

What is the equation associated with the Young’s double slit experiment?

fringe spacing (w) = (wavelength*distance between the screen and slits)/slit separation

What does the interference pattern look like when white light is used?

Gives wider maxima and a less intense diffraction with a central white fringe and alternating bright fringes which are spectra, violet is closest to the central maximum and red furthest

What safety precautions should be in place when using lasers?

Wear laser safety goggles

Don’t shine the laser at reflective surfaces

Display a warning sign

Never shine the laser at a person

What evidence does the Young’s double slit experiment provide?

The wave nature of light because diffraction and interference are wave properties and so proved that EM radiation must act as a wave which disproves the theory that light was formed of tiny particles

What is diffraction?

The spreading out of waves when they pass through or around a gap

When does the greatest diffraction occur?

When the gap is the same size as the wavelength

What happens when the gap is smaller than the wavelength (diffraction)?

Most waves are reflected

What happens when the gap is larger than the wavelength (diffraction)?

There is less noticeable diffraction

What happens when a wave meets an obstacle?

There is diffraction round the edges, the wider the obstacle compared to the wavelength, the less diffraction

How can the width of the central maximum be varied?

Increasing the slit width decreases the amount of diffraction so the central maximum becomes narrower and its intensity increases.

Increasing the light wavelength increases the amount of diffraction as the slit is closer in size to the light’s wavelength therefore the central maximum becomes wider and its intensity decreases

What is a diffraction grating?

A slide containing many equally spaced slits very close together.

What happens when monochromatic light is passed through a diffraction grating?

The interference pattern is much sharper and brighter than it would be after being passed through Young’s double slit because there are many more rays of light reinforcing the pattern. This means the measurements of slit widths are much more accurate as they are easier to take.

What is the zero order line?

The ray of light passing through the centre of a diffraction grating

What is the formula associated with diffraction gratings?

distance between slits * sin(angle to normal made by the maximum) = order*wavelength

What happens to the interference pattern from a diffraction grating when the wavelength increases?

The distance between the orders will increase because the angle is larger due to the increase in diffraction as the slit spacing is closer in size to the wavelength this means the pattern will spread out

How is the formula dsin(θ) = nλ derived?

When the path difference between 2 adjacent rays of light is 1 wavelength the angle between the normal to the grating and the ray of light is θ.

A right angle triangle is formed with side lengths d and λ.

Using trigonometry the first maximum will be when sin θ = λ/d for the first order

The other maxima occur when the path difference between the two rays of light is nλ, where n is an integer, therefore the equation can be generalised by replacing λ with nλ to get: d sinθ = nλ

What are the applications of diffraction gratings?

Light from stars can be split up to get line absorption spectra which can be used to show which elements are present in the star

X-rat crystallography is where x-rays are directed at a thin crystal sheet which acts as a diffraction grating to form a diffraction pattern because the wavelength of x-rays is similar in size to the gaps between atoms. This diffraction pattern can be used to measure the atomic spacing in certain materials

What is a refractive index (n)?

A property of a material which measures how much it slows down light passing through it

What is the equation for refractive index?

refractive index = speed of light/speed of light in that substance

What does it mean if a material has a higher refractive index?

It is known as being more optically dense as light doesn’t slow down significantly when travelling though air (in comparison to travelling through a vacuum

What is refraction?

When a wave enters a different medium causing it to change direction either towards or away from the normal depending on the material’s refractive index

What is Snell’s law?

refractive index₁ * sin(angle of incidence ray₁) = refractive index₂ * sin(angle of refraciton ray₂)

What causes refraction?

As the light moves across the boundary of the 2 materials its speed changes which causes its direction to change

If a substance is more optically dense which way will the light refract?

The ray of light slows down and bends towards the normal

If a substance is less optically dense which way will the light refract?

The ray of light speeds up and bends away from the normal

What happens as the angle of incidence is increased? (refraction)

The angle of refraction also increases until it gets closer to 90*

What is the critical angle?

When the angle of refraction is exactly 90* and the light is refracted along the boundary the angle of incidence has reached the critical angle

What is total internal reflection?

When the angle of incidence is greater than the critical angle and the incident refractive index is greater than the refractive index of the material at the boundary

What is the formula for the critical angle?

sinθ = n₂ / n₁

What is a useful application of total internal reflection?

Optical fibres

How do optical fibres work?

They are flexible, thin tubes of plastic or glass which carry information in the form of light signals. They have an optically dense core surrounded by cladding with a lower optical density allowing total internal reflection to occur. This cladding also protects the core from damage and prevents signal degradation through light escaping the core which can cause information to be lost

What causes signal degradation?

Absorption

Dispersion

What is absorption?

When part of the signal’s energy is absorbed by the fibre reducing the amplitude of the signal which could lead to a loss of information

What is dispersion?

It causes signal pulse broadening which is where the received signal is broader than the original transmitted signal. This can cause signals to overlap causing loss of information

What is modal dispersion?

When light rays entering the fibre at different angles therefore they take different paths along the fibre which leads to the rays taking a different amount of time to travel along the fibre

How can modal dispersion be reduced?

By making the core very narrow therefore making the possible difference in path lengths smaller

What is material dispersion?

When using light of different wavelengths meaning light rays will travel at different speeds along the fibre which leads to pulse broadening

How can material dispersion be reduced?

By using monochromatic light

How can both absorption and dispersion be reduced?

By using an optical fibre repeater which regenerates the signal during its travel to its destination