Waves

Question 1

What are the:

• cycle
• displacement, x
• amplitude, A
• wavelength, λ
• period, T
• frequency, f
• phase
• phase difference

Answer 1

• one complete oscillation of the wave
• how far a point on the wave has moved from its undisturbed position
• maximum magnitude of displacement
• the distance between two identical points on consecutive cycles
• the time taken for a full oscillation
• number of oscillations per second
• the angular distance between a point on a cycle and the start of that cycle
• the angluar distance between two points on a wave, if they were on the same cycle

Question 2

What are the differences between longitudinal and transverse waves (give examples)?

Answer 2

• Transverse waves vibrate at right-angles to the direction of energy transfer. Examples include EM waves, secondary seismic waves & waves on a string
• Longitudinal waves vibrate parallel to the direction of energy transfer. Examples include: Sound waves, primary seismic waves & pulses along a slinky.

Question 3

What is polarisation and how does it provide evidence for the nature of transverse waves?

Answer 3

• Polarisation involves confining the oscillations of a waves to a single plane using a filter placed perpendicular to the direction of propagation.
• The fact that only transverse waves can be polarised shows that oscillation in transverse waves occurs at right angles to the direction of propagation, so a filter placed at right angles to the direction of propagation blocks these oscillations in all but one plane.

Question 4

What are the applications of polarisation?

Answer 4

• Sunglasses have lenses which act as polarising filters. When light is reflected, it is partially polarised. The lenses are orientated to block the plane of oscillation of light reflecting off of horizontal surfaces, reducing glare.
• Radio and TV transmitters produce plane-polarised EM waves, which are recieved with the greatest strength when the recieving aerial is orientated so that it is aligned with the broadcasting aerial.

Question 5

What is the principle of superposition?

Answer 5

When two of more waves interfere, the resulting displacement equals the vector sum of the individual displacements.

Question 6

What is the formula for phase difference?

Answer 6

phase difference = 2πx/λ

If this gives an even multiple of π, reduce it to 2π

If it gives an odd multiple of π, reduce it to just π

For anything else, take away the largest even number possible from the coefficient.

Question 7

How are stationary waves formed and how are they different to progressive waves?

Answer 7

• Superposition of two progressive waves with the same frequency (& wavelength) moving in opposite directions.
• No energy transmitted

Question 8

What are the conditions required for stable interference patterns?

Answer 8

The two wave sources must be coherent:

• same wavelength and frequency
• fixed phase difference

Question 9

How do you tell whether there will be constructive or destructive interference?

Answer 9

if PD = nλ where n is an integer or zero, there will be constructive interference

if PD = (n+1/2)λ, there will be destructive interference

Question 10

What is the formula for the harmonics for stationary waves on strings?

Answer 10

λ = 2L/n

where:

L is the length of the string

n is the number of the harmonic

Question 11

What is the formula for the frequency of the first harmonic in terms of tension, length and mass per unit length?

Answer 11

f = 1/2L * sqrt(T/μ)

Question 12

What is the formula for the wavelength and frequency of stationary sound waves in pipe with 2 open ends?

Answer 12

λ = 2L/n

f_n = nf₁

where f₁ is the frequency of the first harmonic

Question 13

What is the formula for the wavelength and frequency of stationary sound waves in pipe with 1 open end?

Answer 13

λ = 4L/(2n-1)

f_n = (2n-1)f₁

Question 14

Describe how stationary waves are formed in microwave ovens and what effects they have.

Answer 14

• Ovens have metallic surfaces to reflect waves from the magnetron and spread them evenly.
• Stationary waves form as a result of the reflection, resulting in overcooked food at the antinodes and undercooked food at the nodes.
• Microwaves therefore have a rotating turntable to counteract this effect.

Question 15

What is Young’s double-slit formula?

Answer 15

W = λD/s

where:

• W = fringe spacing (constant)
• D = distance between slits and screen
• s = slit spacing (distance between slits)

Question 16

What is the relationship between the width of the central maximum and slit width/wavelength (give formula)?

Answer 16

sin(θ) = λ/a

where:

• θ = angular width of the central maximum
• a = slit width

Question 17

How are slit separation in a diffraction grating and fringe spacing related (derivation needed)?

Answer 17

dsin(θ_n) = nλ

Question 18

Describe the appearance of the diffraction pattern created by shining monochromatic light through a narrow slit.

Answer 18

Bright central maximum with dark and bright fringes alternating on either side, caused by destructive and constructuve interference.

Question 19

Describe the appearance of the diffraction pattern when white light is shone through a small slit.

Answer 19

Different wavelengths are diffracted by different ammounts, with red being diffracted the most (longest wavelength) and blue the least (shortest wavelength).

Theerefore, a coloured spectra is created, with blue at the centre and red on the outside.

Question 20

What are diffraction gratings used for?

Answer 20

• Separating waves into different wavelengths in high res.
• Spectrometers
• Telescopes to analyse light from different bodies
• CD & DVD drives

Question 21

What is the advantage of diffraction gratings with higher slit densities?

Answer 21

There are more beams to reinforce the pattern so the pattern is sharper; the bright bands are brighter and the dark bands are darker.

Therefore, more accurate measurements can be made.

Question 22

Why are lasers dangerous and what can you do to reduce the risk they pose?

Answer 22

• If you looked directly at a laser, your eye’s lens would focus it onto your retina, which would be permanently damaged.
• Never shine a laser toward a person or at a reflective surface
• Have a warning sign on display
• Turn off laser when its not needed

Question 23

What is the equation for the refractive index of a material?

Answer 23

n = c/c_s

where c_s is the speed of light in that material

Question 24

What is the definition of the relative refractive index between two materials?

Answer 24

Ratio of the speed of light in the first material to the speed of light in the second material:

₁n₂ = c₁/c₂

Question 25

What is the formula for the relative refractive index at the boundary between two materials given their absolute refractive indicies?

Answer 25

₁n₂ = n₂/n₁

Question 26

Is the critical angle a lower or upper bound for reflection over refraction?

Answer 26

lower

Question 27

How do step-index optical fibres work?

Answer 27

• High refractive index core surrounded with low refractive index optical cladding, to minimise the critical angle and so maximise the range of angles over which TIR will occur. Cladding also protects from scratches which could let light escape.
• Light is shone in at one end of the fibre, and undergoes multiple TIRs until it reaches the other end.

Question 28

Explain the effect of absorption in optical fibres.

Answer 28

The material of the fibre absorbs some of the energy of the light, so the amplitude of the signal is reduced.

Question 29

Explain the effect of material and modal dispersion in optical fibres.

Answer 29

• Modal dispersion:
  
  • light rays enter the fibre at different angles
  • travel along paths of different lengths
  • take different times to reach the other end
  • pulse broadens
  • Mono-mode fibres allow only one path
• Material dispersion:
  
  • different wavelengths of light will travel at different speeds in the fibre
  • some wavelengths will reach the other end faster than others
  • the pulse broadens
  • using monochromatic light stops this effect

Broadened pulses can overlap and degrade the signal.