A Level Physics (OCR A): Waves

progressive waves (aka travelling waves)

these are waves which transfer energy from one place to another, but not matter - particles of matter oscillate about equilibrium but do not travel with the wave (e.g. sound, light and earthquakes)

transverse waves

waves in which oscillations are perpendicular to the direction of energy transfer (e.g. light, ripples in water, all electromagnetic waves, and S-waves)

longitudinal waves (aka compression waves)

waves in which oscillations are parallel to the direction of energy transfer (e.g. sound waves and earthquake P-waves) - they have alternate compressions and rarefactions of the medium through which the wave is travelling

displacement (S(m))

the distance from the equilibrium position in a particular direction; a vector, so it can have either a positive or negative value

amplitude (A(m))

the maximum displacement from the equilibrium position; it can be positive or negative

wavelength (λ(m))

the minimum distance between two points in phase on adjacent waves (e.g. the distance from one peak to the next, or from one compression to the next)

time period of oscillation (T(s))

the time taken for one compete oscillation; the time taken for a wave to move one whole wavelength past a given point

frequency (f(Hz/s^-1))

the number of wavelengths passing a given point per unit time

phase difference

the amount by which one wave lags behind another wave

phase

A measurement of the position of a certain point along the wave cycle

relationship between frequency and time period

they are inverse; 1 = T x f

wave speed (V or c (ms^-1))

the distance travelled by the wave per unit time; wavelength x wave frequency

phase difference (measured in degrees or radians)

The amount one wave lags behind another as a proportion of the wavelength.

oscilloscope (cathode ray)

Measures voltage, displaying waves from a signal generator as a function of voltage over time - these waves are called traces. Sources of waves could be produced by plugging in an AC supply; or a microphone which converts sound waves into electrical signals.

markings on an oscilloscope

Vertical divisions = voltage/amplitude of the wave (controlled by gain dial)
Horizontal divisions = time (can be used to find time period and frequency; controlled by timebase dial).

wave refraction

when a wave bends at a boundary between two materials due to the difference in density causing it to speed up or slow down

polarised waves

waves oscillating along only one axis

unpolarised waves

waves oscillating in any direction perpendicular to the axis of propagation

plane of polarisation

the plane in which the wave vibrates

plane polarisation

when a plane is polarised so that it only oscillates in one direction, e.g. using a polarising filter - this is only possible for transverse waves

investigating polarisation using two filters

- shine unpolarised light through two filters
- align their transmission axes so that they are both vertical
- keep the position of the first filter fixed and then rotate the second one through 180 degrees
- at first, all of the light passing through the first filter passes through the second, but as it rotates, less light will get through, decreasing the intensity
- at 45 degrees, this will have decreased to half the intensity, and at 90 degrees no light will pass through, so the intensity would be zero
- as you continue turning, the intensity of the light would start to increase again, and the two will align at 180 degrees, so all of the light would pass through the second filter
- this is because you could think of the transmission axis of the filter as having vertical and horizontal components, so as the vertical component increases, more vertically polarised light would pass through the filter

investigating polarisation of microwaves

- metal grilles must be used instead of polarising filters because the wavelengths of microwaves are much larger
- place the metal grille between a microwave transmitter and receiver, with the two facing each other, and connect the receiver to a voltmeter
- as transmitters already produced vertically polarised microwaves, there is no need to use a second filter
- the intensity of microwaves will be the greatest when the direction of vibration of the waves and the grille are at right angles to each other
- when the grille is rotated, the intensity of the waves passing through the grille would decrease, causing the voltmeter reading to decrease
- when the wires are aligned with the direction of the polarised waves, no signal would be shown because the grille is absorbing their energy completely
- this is because the EM wave's vibrating electric field excites electrons in the metal grille, causing the energy of the microwaves to be absorbed and re-emitted in all directions
- this means that very few of them are vibrating in the direction of the receiver (vertically), and as the receiver only receives polarised waves, the few microwaves in the correct direction may not even be picked up, causing a drop in intensity
- however, when the metal grille is horizontal, less electrons will be excited vertically, so less waves will be absorbed and re-emitted in random directions - most will continue to be vertical

investigating diffraction using a ripple tank

- Create water waves in the tank using an oscillating paddle, which dips in and out of the water to create waves with straight, parallel wave fronts
- Place objects into the ripple tank to create a barrier and a gap in the middle, and vary the size of the gap for them to pass through.
- Note how the direction of the waves passing
through changes - when the gap is a lot larger than the wavelength, diffraction is unnoticeable, but this increases with gaps several wavelengths wide. The most diffraction occurs when the gap is the same size as the wavelength

investigating diffraction in light

- for laser, it can be shined through a very narrow slit onto a screen, which would give you a pattern of light and dark fringes (as long as the wavelength is roughly equal to the slit spacing). There would be a bright central fringe with alternating dark and bright fringes, and the narrower the slit, the wider the diffraction pattern
- this could be repeated using white light instead of monochromatic lasers, and colour filters could be used to vary the wavelength of the light whilst the slit spacing is kept constant

wave diffraction around obstacles

where waves meet obstacles, they will diffract around the edges, but there would be a shadow behind the obstacle where the wave is blocked - the wider the obstacle compared to the wavelength, the less diffraction that would occur, so the longer the shadow

reflection

when waves are bounced back after hitting a boundary and the angle of incidence is equal to the angle of reflection

investigating wave reflection using a ripple tank

- using a square setup in the ripple tank, use an oscillating paddle to create regular waves with straight, parallel wavefronts
- place a barrier at an angle to the incoming wavefronts, and they should be reflecting off the barrier and travelling away in a different direction
- the angle of incidence can be changed by rotating the barrier, and the angle of reflection should adjust accordingly so that the two are equal

intensity (eqn i.t.o power)

power / area

intensity

the rate of flow of energy per unit area at right angles to the direction of travel, measured in Wm^-2

relationship between intensity and amplitude

Intensity is proportional to amplitude2 - this is because intensity is proportional to energy, and the energy of a wave depends on amplitude^2

speed of EM waves in a vacuum

3 x 10^8 m/s ('the speed of light')

range of wavelengths for visible light

300-700nm.

refraction

when a wave changes direction as it enters a different medium - it will bend towards the normal when slowing down (entering a more optically dense medium) and will bend away from the normal when speeding up (entering a less optically dense medium) - this is because the wavelength of the wave is changing and the frequency stays constant

investigating refraction using a ray box and a glass block

- trace the glass block's outline onto a piece of paper
- shine a beam of light into it using a ray box
- trace the path of the incoming and outgoing light
- remove the block and draw in the path of light inside the block, and draw normals at the points of entry and exit
- then, measure the angles of incidence and refraction
- use Snell's law n1 sin i = n2 sin r to find the refractive index, n2 of the material the light enters, assuming that n1 = 1 in air

wave speed

frequency x wavelength

refractive index

the ratio between the speed of the wave in a vacuum, c, and the speed of the wave in the medium, v. Therefore, n = c/v.

refractometer

a device used to accurately measure a material's refractive index by shining a beam of light through a sample, which could then be viewed through a microscope to measure the angle of refraction

refractive index (eqn)

c (speed of light) / v (velocity in the material)

critical angle

the angle of incidence at which the light will reflect off a boundary rather than refracting in the medium

critical angle (eqn)

sinC = 1/n (refractive index)

investigating critical angles and total internal reflection

- shine light into the curved face of a semicircular glass block so that it enters at right angles to the edge, so it does not refract as it enters the block but does once it reaches the straight edge
- vary the angle of incidence until the light beam refracts so much that I exits the block along the straight edge to find the critical angle C
- beyond this point, refraction is impossible, so all of the light is reflected back into the material (total internal reflection)

superposition

When two waves meet, the resulting displacement is the sum of the individual displacements.

principle of superposition

When two or more waves meet, the resultant displacement equals the vector sum of the individual displacements.

constructive interference

The interference that occurs when two waves combine to make a wave with a larger amplitude - this will happen when the two waves are in phase, so they are at the same point in a wave cycle (phase difference = 0 or multiple of 360)

destructive interference

The interference that occurs when two waves combine to make a wave with a smaller amplitude; and the two waves must be perfectly out of phase (at odd multiples of 180)

path difference for constructive interference

nλ

path difference for destructive interference

(n+0.5)λ

investigating superposition using sound

● Use two speakers, a moderate distance apart, connected to the same signal generator (oscillator) to transmit sound waves.
● Walk along a line perpendicular to the speakers - you should hear alternating loud and quiet points.
● This is because in some places the waves from each speaker constructively interfere (loud) and in some places it's destructive.

coherence

When waves have the same frequency and wavelength and a fixed phase difference between them (often zero in exam questions).

path difference

the difference in distance that two waves have travelled in terms of the wavelength (units of length)

why are lasers used in experiments?

they produce monochromatic (same wavelength/colour) light

Young's double slit experiment

A single source of light directed towards a double slit, which creates two coherent beams of light. This interferes as it hits the screen and creates an interference pattern.

investigating two-source interference

- Light needs to be coherent and monochromatic, and the slits must be a similar size to the wavelength
- the light is then diffracted from the two slits, which act as two coherent point sources
- this gives a pattern of light and dark fringes, and to measure the fringe spacing we can measure the length of several fringe spaces and then divide it by the number of dark and light fringes to lower the percentage error, x
- measure the distance between the source and the screen, D
- measure the spacing between the slits, a
- then use the formula x = λD/a to calculate the wavelength of the light, which should be between 400-700nm

evidence for the wave nature of light

By showing that light is able to both diffract and interfere, which are both uniquely wave properties.

investigating diffraction gratings

by repeating Young's double slit experiment with a diffraction grating, you would get the same pattern but with brighter and narrower bright fringes and darker dark fringes - the interference pattern is actually sharper because many beams reinforce the pattern, and the sharper fringes are more precise and easier to measure:

using a laser, the maxima would be sharp lines between which the fringe width, x, could be measured, with each of the maxima being order lines (n), and the distance between the source and the screen being D. Then, the angle theta could be measured between the source and the order line (the incident light), and we could find the slit separation for the diffraction grating by dividing 1 by the number if slits per metre. Following small angle approximations, the formula d sin theta = nλ could be used to find the λ

wavelength of light (eqn i.t.o split spacing and distance to the screen)

( a (split spacing)* x (fringe spacing)) / D (distance to screen)

maximum number of fringes produced

n (number of fringes) * λ (wavelength) = D (distance) sinθ (between central maxima)

diffraction of white light

produces a mixture of colours, with the 0th order remaining white and each order becoming a spectrum, with red light being diffracted the most compared to violet light because it has a much larger λ and λ is proportional to sin theta

stationary waves

waves that consist of alternating fixed pattern of nodes (points with zero amplitude) and antinodes (points with maximum amplitude). No energy is transferred across the wave.

stationary waves on a string

By attaching a vibration transducer on one end of a stretched string when the other end is fixed, this can create a wave by vibrating the string according to a given wave frequency from a signal generator. By alternating the signal generator a bit, it can be adjusted so that there is an exact number of waves in time in which it gets to one end and back, so that the original and reflected waves reinforce each other at resonant frequencies - this would cause an exact number of half λs to fit onto the string. Each particle vibrates at right angles to the string.

node

A point with no vibrations in which the resultant amplitude is 0.

antinode

A point with maximum vibration in which the resultant amplitude is at maximum.

requirements for a stationary wave

- coherent waves
- must be travelling in opposite directions

stationary wave experiment example

Use an oscillator to pass a wave along a string which is fixed at one end.
The stationary wave will form when the progressive wave is reflected off the fixed end.

similarities between stationary and progressive waves

both have wavelength, frequency and an amplitude

key difference between stationary and progressive waves

in stationary waves, energy is not transmitted from one place to another

first harmonic

when a standing wave is operating at the lowest possible resonant frequency, with only half λ

resonance tube stationary wave experiment

- Create a closed end pipe using a hollow pipe inside a measuring cylinder containing water.
- Use a tuning fork (producing known frequency) and hold it above the tube, noting down the frequency of sound it produces. Then, gently tap it on top so that the sound waves travel down the tube and get reflected, forming a node at the water surface. NOTE: the actual node would be formed slightly above the end of the tube, so this may be added on as a correction value
- Move the tube up until you find the first position which causes resonance (this should be the shortest distance between the top of the tube and water level where the fork resonates)
- This length will be a quarter of the wavelength.
- Use speed = frequency x wavelength.

harmonic

a point where the stationary wave form doesn't change because the waves in each direction are reinforcing each other

stationary waves in wind instruments (or other air columns)

At some frequencies, resonance occurs so a stationary wave would be set up, with nodes forming at the closed end of instruments (usually with the lowest frequency at λ/4), and antinodes forming at the open ends of piper (where both ends are open, the lowest resonant frequency would be at λ/2).

stationary waves with microwaves

Microwaves could be produced by a microwave transmitter, which would therefore lead to them being reflected off a metal reflecting plate back towards the transmitters, and as the distance between the two is adjusted, the waves can interfere and set up a stationary wave, and the nodes/antinodes could be found by moving the receiver between the two.