A-level Physics Paper 1: Waves and Combining Waves

Progressive waves

An oscillation or vibration that transfers energy in the direction of propagation

Amplitude of a mechanical wave

The maximum displacement of particles from their undisturbed positions

Phase of a progressive wave

The position of a certain point on a wave cycle relative to the start of the cycle

In phase (progressive wave)

2 points on a wave that are moving at the same speed in the same direction

Out of phase (progressive wave)

2 points on a wave that are moving at different speeds or in a different direction

In antiphase (progressive wave)

2 points on a wave that are moving at the same speed but in opposite directions

Longitudinal waves

A wave with oscillations that are parallel to the direction of energy propagation

Transverse waves

A wave with oscillations that are perpendicular to the direction of energy propagation

Electromagnetic waves

Travel at the speed of light in a vacuum, with magnetic and electric fields vibrating at right angles to each other and the direction of propagation

Superposition

When 2 waves of the same type meet at the same point and overlap, causing the resulting displacement of the oscillations to be the sum of the displacement of each wave

Coherent sources

Waves from each source have the same wavelength and frequency, and there is a constant phase relationship between the sources

How to determine whether 2 coherent waves will constructively or destructively interfere

If the path difference is nλ, then it will constructively interfere. If the path difference is (n+1/2)λ, then it will destructively interfere.

Diffraction

When waves spread around an obstacle or gap, which is more pronounced if the wavelength of the wave is similar to the size of the gap. The wavelength doesn't change, but the wave itself curves and spreads into shadow regions

Diffraction gratings explanation (5)

Consists of a large number of equally spaced parallel slits; when light hits the slits, it diffracts through every slit simultaneously, spreading out in all directions; waves from slits overlap and undergo interference; constructive interference only occurs at specific angles where the path difference between adjacent slits is nλ, producing very sharp and bright fringes separated by large dark regions

How are individual maxima produced by a diffraction grating different to those from double slit, and why

They are sharper, as more slits leads to greater reinforcement of constructive interference and narrower regions of reinforcement

How to find maximum number of possible orders (n) for a given diffraction grating

Set θ = 90°, so n=d/λ. Round DOWN to nearest integer

Appearance of central fringe when white light passes through diffraction grating or double slit, and why

bright white fringe, as all wavelengths have zero path difference at the center

Appearance of side fringes when white light is used in a diffraction grating

A spectrum of colours, where violet is closest to the center and red is furthest from the center

Uses of diffraction gratings

Atomic emission spectroscopy, space telescopes, CDs and DVDs

Refraction

When light travels at any angle other than along the normal between 2 media of differing refractive indices, and changes speed, wavelength, and path (bending towards or away from the normal) without changing frequency

What changes and what stays the same when a wave is refracted

Speed and wavelength changes, frequency doesn't change

Refractive index equation

n=c/v

Relative refractive index equation

1n2 = n_1/n_2

Snell's law

n_1sin(θ_1)=n_2sin(θ_2)

Total internal reflection

The complete reflection of waves back inside a medium at a boundary with a second material in which the material travels faster

Critical angle

The angle of incidence at which the angle of refraction is 90°

Optical fibre

A thin glass or plastic fibre that transmits light, trapped by repeated total internal reflection

Structure of a step index optical fibre

Central core with a uniform refractive index, cladding with a smaller refractive index for TIR and protecting the core, sheath to prevent light leakage into other optical fibres

Disadvantages of pulse broadening

Decreases the maximum bandwidth along the optical fibre

Material dispersion

Different wavelengths travel at different speeds, so a sharp pulse undergoes pulse broadening into a broader signal, solvable with monochromatic light

Modal dispersion

Rays inside an optical fibre take slightly different paths, and rays that take longer paths take longer to travel through the fibre, so the duration of the pulse increases and the pulse broadens, solvable with monomode fibres with a very narrow core

Consideration due to absorption in an optical fibre

The material must have a low absorption at the wavelength used to send materials, and it may be necessary to amplify the signal for longer distances

Advantages of optical fibres over copper cables

Faster transmission, cheaper to manufacture, less energy loss through heat

Reason for destructive interference in single-slit diffraction of monochromatic light

Light from one part of the slit diffracts, overlaps, and interferes with light that has diffracted from other parts of the slit, and so whether a given point will be a maximum or a minimum can be determined by determining the path difference between the top compared to the bottom of the slits to the screen

Equation for the angle at which the first minimum occurs in single-slit diffraction

sin(θ)=λ/a, where a is the slit width

What is wavelength

The shortest distance between 2 points in phase

What is amplitude

The maximum displacement from the rest/equilibrium position

Why might some minima in Young's Double Slit not have zero brightness

Intensity decreases with distance, and one of the waves may be travelling further than the other, so although there is destructive interference from the waves being in antiphase as the point of intersection, the amplitudes might not be exactly equal

Why might a radio station not have issues with buildings and hills blocking the path

High wavelength means that there is a greater diffraction, with buildings and hills being quite large obstacles, but the large diffraction leading to a smaller region of shadow

How best to measure the time taken for a ripple of water to travel a certain distance, instead of using a stopwatch

Use a video camera with a scale, and the recording can be replayed and looked at frame by frame, and the reaction time error is eliminated with a video

Appearance on screen of single-slit diffraction of monochromatic light

Central maximum, surrounded by less bright subsidiary maxima. Symmetrical on both sides. Width of central maximum is twice that of the subsidiary maxima

(ASSUME THAT THE SLIT WIDTH IS GREATER THAN OR EQUAL TO RED WAVELENGTH) Appearance on screen of single-slit diffraction of chromatic light

Central white fringe, subsidiary maxima are composed of a spectrum, where violet is closer to the central maximum and red is further from the central maximum. Maxima are wider than those found in monochromatic single-slit diffraction patterns

Compressions

Point just after peaks, regions of high pressure in a longitudinal wave

Rarefactions

Point just after troughs, regions of low pressure in a longitudinal wave

Polarisation

The process by which the oscillations of a transverse wave are restricted to a single plane

What determines the direction of polarisation of an EM wave

The orientation of the electric field

Important consideration when setting up radio aerials

The transmitting and receiving aerial must be oriented in the same direction, due to the direction of polarisation of the emitted EM wave being dependent on the orientation of the transmitting aerial

If unpolarised light passed through a polarising filter, how much energy would pass through

Half of the energy would pass through on average

What happens to light when it's reflected

The reflected rays are polarised parallel to the reflective surface, perpendicular to the normal

Polarisation with sunglasses

The lenses include vertical polarising filters, which block out the reflected light rays from horizontal surfaces, like snow for skiers or roads for drivers

Polarisation with multiple EM aerials

If 2 transmitting aerials are in close proximity to one another, the aerials can be oriented to be perpendicular to each other, and due to the polarised nature of the propagated EM waves, there will be minimal interference

Noise cancelling earphones

A microphone records background noise, some circuitry inverts the wave, and it is propagated into the ear so that it destructively interferes with the background noise

How does constructive interference occur to form a maxima

2 waves with the same amplitude and direction superpose, so the resulting amplitude is the sum of both amplitudes

How does destructive interference occur to form a minima

2 waves with the same amplitude but opposing directions superpose, so the resulting amplitude is 0

Young's Double Slit description (3 points)

Coherent light source illuminates 2 closely spaced narrow slits; Light passes through slits and diffracts, causing the two emerging wavefronts to overlap; the waves undergo superposition to form an interference pattern on a screen consisting of equally spaced bright and dark fringes.

Why is a single slit placed before the double slit in Young's Double Slit (if not using a laser)

To ensure the light reaching the double slits is coherent with a constant phase relationship

What causes the bright and dark fringe patterns in Young's Double Slit

Constructive interference with path difference nλ (in phase) forms maxima, and destructive interference with path different (n+1/2)λ (out of phase) forms minima

What is w=λD/s

Fringe spacing for double slit. w is fringe spacing (distance between adjacent maxima), D is distance from slits to screen, and s is separation between centres of two slits

Determining whether 2 points are in phase and in antiphase (stationary waves)

If they are both between the same adjacent nodes, they are in phase. If they are on the opposite sides of a node, they are in antiphase

Harmonics

The different modes of vibration that can occur in a stationary wave, where the fundamental frequency is the lowest frequency of vibration

Drawing harmonics in fixed-fixed, fixed-open, and open-open ends

Nodes must be at fixed ends, antinodes must be at open ends

Experiment for the variation of frequency for stationary waves on a string

Measure mass and length of string, then find mass per unit length. Set up vibrating source on a workbench, with a pulley on the end, and connect one end of the string to the vibrating source, and the other end to a load of known weights over the pulley. Adjust the frequency of the vibrations until stationary waves form. Adjust length of string and adjust frequency to form stationary waves again, keep repeating, and use the equation to find the frequency.

Microwaves and stationary waves

Microwaves can form stationary waves when they reflect off metallic inner surfaces, which can lead to food being overcooked at the antinodes and undercooked at the nodes, so a rotating turntable is used to evenly cook the food. This effect can be visualised by removing the turntable and placing chocolate, then using the microwave and observing the regions where it has melted more

Amplitude for stationary wave vs progressive wave

Each point on a wave has the same amplitude for a progressive wave but a different amplitude for a stationary wave

Phase for stationary wave vs progressive wave

Adjacent points vibrate with different phase in a progressive wave, but all points between nodes vibrate in phase in a stationary wave

Energy transfer for stationary wave vs progressive wave

Progressive waves transfer energy through space in the direction of propagation, stationary waves don't transfer energy through space

Conditions for the formation of a stationary wave

The superposition of 2 progressive waves of the same frequency and wavelength, with similar amplitudes, travelling in opposite directions with equal but opposite velocities. This leads to the formation of nodes, or minima, where destructive interference occurs and there is the least oscillation as the waves are in antiphase leading to zero amplitude, and the formation of antinodes, or maxima, where constructive interference occurs and there is the most oscillation as the waves are in phase leading to maximum amplitude

What happens to the receiver signal when you rotate the transmitter of an EM wave 90°

EM waves from the transmitter are polarised, so rotating the transmitter rotates the plane of polarisation, and the receiver signal becomes zero when the receiver is perpendicular to the plane of polarisation

How do you know that a stationary wave on a string is transverse

The displacement of particles is perpendicular to the rest position of the string

For a fixed-fixed stationary wave, as you modify the frequency, what happens to the number of antinodes

The number of antinodes will follow, e.g. 3frequency means 3antinodes:

What is particle displacement for a sound wave

Distance of a particle from the equilibrium position in the direction of energy transfer

How must the transmitting and receiving EM aerials be aligned

State that the transmitting and receiving aerials must be aligned in the same plane of polarisation of the wave

When talking about signal strength changing as you move along, like the speakers in the classroom example, say that

The waves from the 2 sources superpose at a point, where there's no phase difference at maxima, but there's a phase difference at minima

Why aren't there any dark bands when perpendicular polarising filters are placed over the slits in Young's Double Slit

Oscillations of light from the 2 filters are perpendicular to each other, so the waves don't interfere, so zero amplitude is not possible

How is a bright line formed by a diffraction grating at the first-order diffraction angle

Light from each slit superposes, and light from adjacent slits have a path difference of one wavelength, and at this angle all waves are in phase so they constructively interfere.

What is it called when light is reflected on the inside yet total internal reflection does not occur (not fully reflected internally)

Partial reflection

Why is diffraction less pronounced when the wavelength is smaller than the size of the gap

With dsin(θ)=nλ, as λ decreases, so does sin(θ) and therefore θ.

Young's Double Slit with white light

White central fringe, and every other fringe is a spectrum with violet closer to the center and red further from the center. Fringes become wider and less distinct as you move further from the center

How does increasing slit width affect the single-slit diffraction pattern

Narrower central maximum, lower intensity

What is the consequence of pulse broadening

Pulse overlap, leading to loss of data/corruption