Waves

Waves AQA

What is a mechanical wave?

Oscillation of particles, that require a medium to travel

What is an electromagnetic wave?

Oscillations of fields, that do not require a medium to travel

What is a longitudinal wave?

The direction of oscillations are parallel to the direction of energy transfer

What is a transverse wave?

The direction of oscillations are perpendicular to the direction of energy transfer

What is polarisation?

The process of forcing a transverse wave’s oscillations to one plane only.

What does it mean if a wave is unpolarised?

Oscillations can change from one plane to another

What does a polarising filter do?

It only allows light through that oscillates in a certain plane and direction - hence polarises it.

Explain what it means if 2 polaroid filters are ‘crossed’

Crossed suggests that the 2 filters are at an angle of 90* to each other. When light passes through the first filter, the particles are polarised, and are not at 90* to the direction of the plane that the second filter polarises through. Therefore, the light cannot pass through the second filter, and the light intensity reduces to a minimum.

How do polaroid sunglasses work?

They reduce the glare of reflected light from the sun, by containing a polaroid filter, which polarises light to a specific plane, and reduces the light intensity.

What is the displacement of a vibrating particle?

distance and direction from equilibrium position

What is the amplitude of a vibrating particle?

the maximum displacement

What is the wavelength of a wave?

the smallest distance between 2 adjacent vibrating particles with same displacement and velocity

What is a cycle?

one max displacement to the next max displacement

What is a period?

time for one complete wave to pass a fixed point

What is the frequency of a wave?

number of complete waves passing a point per second

If the wave has a large wavelength, what is the relative size of the frequency?

It is small

What is the phase of a vibrating particle?

the fraction of a cycle it has completed since the start of the cycle

What is the phase difference of two particles at the same frequency?

fraction of a cycle between the two particles

What is the size of 1 cycle in degrees and radians?

360* or 2π

What is the formula for the phase difference?

2πd/λ

What is the principle of superposition?

when two waves meet, the total displacement at a point is equal to the sums of the individual displacements at that point. They have to be travelling in opposite directions.

Outline and explain the different combinations of superposition.

• crest + crest = supercrest (reinforcement)

• trough + trough =supertrough (reinforcement)

• crest + trough (of same amplitude) = minimum (cancellation)

What is interference?

When waves pass through each other at a constant frequency and phase difference, and cancellation/reinforcement occurs in fixed positions.

What are coherent sources of waves?

They produce an interference pattern when they overlap, because they vibrate at the same frequency and a constant phase difference.

What would happen to the interference pattern if the phase difference of 2 coherent waves changed at random?

The points of cancellation and reinforcement would change at random, so the interference pattern would not be seen.

How is a stationary wave formed?

A progressive wave is produced at one end of a string. A wave reflects back, and these 2 waves are travelling in opposite directions, with the same frequency. When they meet, they superpose and interfere constructively at antinodes and destructively at nodes (max displacement at antinodes, and minimum at nodes). Important to note that these nodes are at fixed points along the wave.

What is a node?

A point of minimum displacement, and hence 0 energy

What is an antinode?

A point of maximum displacement, and hence maximum energy

Describe the first harmonic.

It is a wave on a string that vibrates at the fundamental frequency. It contains 2 nodes, and 1 antinode. The Length is equal to half lambda. The frequency is equal to the speed divided by 2 x the length.

How can we form the second harmonic from the first harmonic?

We increase the frequency by 2x, and therefore half the total wavelength

Explain why stationary waves do not transfer energy.

At nodes, the amplitude of vibration is 0. At antinodes, the amplitude of vibration is maximum. These points are in fixed positions, therefore no energy can be transferred.

What are the properties of frequency of a stationary wave compared to a progressive wave?

In stationary, all the particles vibrate at the same frequency, except those at nodes - in progressive, all particles vibrate at the same frequency no matter its position.

What are the properties of amplitude of a stationary wave compared to a progressive wave?

In stationary, amplitude varies from 0 at nodes, to maximum at antinodes - in progressive, all particles have the same amplitude.

What are the properties of phase difference of a stationary wave compared to a progressive wave?

In stationary, phase difference is equal to mπ, where m is the number of nodes between the 2 particles - in progressive, phase difference is equal to 2πd/λ.

What is the definition of the first harmonic?

The lowest frequency that produces an interference pattern on a stationary wave.

Describe the second harmonic.

It consists of 3 nodes, and 2 antinodes.

L = λ

f = c/L

Describe the third harmonic.

It consists of 4 nodes, and 3 antinodes.

L = 3λ/2

f = 3C/2L

Explain the relationship between the frequencies of the first harmonic, the second harmonic, and the third harmonic.

Second harmonic frequency = 2 x first harmonic

Third harmonic frequency = 3 x first harmonic

How can you calculate the length of a vibrating portion of a string?

L = mλ/2 (where m is the number of nodes in the portion of vibrating string)

Explain what effects pitch.

High frequency = high pitch

Low frequency = low pitch

How can you change the pitch?

Increase pitch - increase tension/shorten length

Decrease pitch - decrease tension/increase length

what is the value of µ

It is the mass per unit length of the string

What is refraction?

It is the change in direction that occurs when light passes at an angle across a boundary between 2 transparent surfaces

Describe what happens when light waves enter a glass medium from air (in terms of refraction)

The ray bends towards normal - slows down (because air is less dense, and glass is more dense)

Describe what happens when light waves enter air from a glass medium (in terms of refraction)

The ray bends away from normal - speeds up (because its moving from a dense medium to a less dense medium)

What are the respective speeds of light in air and glass

• air = 3×10^8

• glass = 2×10^8

What happens to light if it passes into a more dense substance?

The ray slows down, (the wavelength decreases), and so it bends towards the normal

What happens to light if it passes into a less dense substance?

The ray speeds up, (the wavelength increases), and so it bends away from the normal

Describe two key features of refraction from air to glass.

• Angle of refraction is always less than angle of incidence.

• Partial reflection also occurs.

What is Snell’s law?

n1sinθ1 = n2sinθ2

What is the absolute refractive index?

The ratio between speed of light in a vacuum to speed of light in a material - always greater than 1, as no material is less optically dense than a vacuum

What is the relative refractive index?

The ratio between the speed of light in one material compared to the speed of light in another - can be greater than 1

What does the amount of refraction depend on?

The speed of light in each substance (so the smaller the speed of light in a substance, the greater the refractive index of the substance because Ns = C/Cs)

Explain what happens to the frequency, wavelength and speed of a wave when it passes through the boundary of two transparent substances at an angle.

The frequency of the wave DOES NOT CHANGE when refraction occurs, but the wavelength does. so Ns = λ/λs (where λs is the wavelength of the wave in the substance).

What is the approximate refractive index of light in air?

1 (1.0003)

Explain the white light spectrum.

White light is a combination of all the different wavelengths of visible light - spanning from red (650nm) - violet (350nm).

Explain dispersion and the dispersive effect of a prism.

Dispersion happens due to the refraction of white light. The prism refracts the light at different amounts depending on the wavelength. The Shorter the Wavelength (in air) the greater the refraction, so each colour is diffracted by a different amount, and the speed of light in glass depends on wavelength (slower = lower wavelength = greater refraction).

If a ray of light moves from glass to air, what is observed if the angle of incidence = critical angle?

It refracts across the boundary of the glass at 90* to the normal (and there is still some partial reflection - as partial reflection always occurs when the angle of incidence is less than or equal to the critical angle)

What happens if the angle of incidence is greater than the critical angle?

Then the ray undergoes total internal reflection (same as reflection of a mirror)

What are the 2 requirements for total internal reflection to take place?

The incident substance should have a larger refractive index than the other substance

The angle of incidence should be greater than the critical angle

Explain why diamonds sparkle.

• Light enters diamond - splits into the colours of the spectrum

• Very high refractive index, so the colours are separated a lot

• Because of the high refractive index, the ray of light undergoes total internal reflection many times before it emerges from the diamond

• so the colours disperse more and more, and the diamond sparkles with many colours

How does an optical fibre work, and why may it not work in some cases?

A light ray is totally internally reflected each time it reaches the fibre boundary, because the angle of incidence exceeds the critical angle of the fibre. It might not reflect totally if the radius of the bend of the fibre is too small.

Describe in brief terms how optical fibres work for communications.

Pulses of light enter from one end at a transmitter, and reach a receiver at the other end.

Explain the required characteristics of the fibres, and why they are needed to be like that.

• Fibres need to be highly transparent to avoid the absorption of light (absorption can continuously reduce the amplitude of the light)

• Each fibre consists of a core surrounded by a layer of cladding. The cladding has a lower refractive index to reduce light loss from the core (as this could reduce the amplitude of the light pulses)

Explain why the cladding is needed around the core.

Total Internal Reflection takes place at the core-cladding boundary. If there was no cladding, the light would cross from one fibre to the other if 2 fibres are in contact - signals would corrupt and be insecure, as would reach the wrong destination.

Explain how the width of the core upholds proper message transmission.

The core should be narrow to prevent modal (multipath) dispersion - it happens in a wide core because the light travelling along the axis of the core travels a shorter distance per metre of fibre compared to a ray that is repeatedly totally internally reflected. Also, a pulse of light sent via a wide core would become longer than it was supposed to be, and if it is too long, it may merge with the next pulse

Other than Modal dispersion, give another example of pulse dispersion and explain why it may arise.

Material/spectral dispersion. Occurs if white light is used instead of monochromatic light. (the speed of light in the optical fibre depends on the wavelength of light. Violet travels slower than red in glass, and so the difference in speed causes the white light pulses to become longer - as the violet component falls behind the red component - so we must use monochromatic light)

How many bundles of fibres does a medical endoscope contain?

2 bundles

Explain how the visibility of the body cavity is increased using one of the bundles of fibres.

it is inserted into a body cavity, and illuminated using light sent through one of the bundles

Explain how an image is formed using the other bundle of fibres.

A lens over the other bundle is used to form an image of the cavity on the end of the bundle - the light then travels in pulses to the other end of the bundle, where the image is observed. The bundle must be a coherent bundle.

What is a Coherent Bundle?

Fibres at each end are in the same relative position.

What are Young’s Fringes?

Alternate bright and dark fringes that can be seen on a white screen due to where diffracted light from the double slits interfere

What happens if the single slit is too wide?

The dark fringes become narrower than the bright fringes, and contrast is lost between light and dark fringes.

How is a bright fringe produced?

Light from one slit reinforces light from the other, and they arrive to the screen in phase with each other

How is a dark fringe produced?

Light from one slit cancels light from the other, and they arrive to the screen πrads out of phase

Give 3 ways to increase fringe width.

Increase wavelength

Increase distance

Decrease slit spacing

What type of waves do the double slits emit?

Coherent Waves (the double slits are hence a coherent source)

Why would 2 lightbulbs not produce coherent waves?

The 2 sources emit waves at random, so the points of cancellation and reinforcement would change at random.

Give a characteristic of the wave that can affect the fringe separation.

The colour (e.g red - longest wavelength - greatest separation)

Describe how white light produced fringes appear.

Central fringe is white. Inner fringes are blue, Outer fringes are red (red fringes are more spaced out than blue fringes)

What are the respective path differences of a bright fringe and dark fringe?

Bright = nλ
Dark = (n+1/2)λ