Waves Flashcards
What is the equation for wave speed?
Wave speed (ms^-1) = frequency (Hz) x wavelength (m) c = f λ
What is the equation for frequency?
Frequency (Hz) = 1 / time period (s)
f = 1/T
What happens when a wave is reflected?
The wave hits the boundary at the angle of incidence, and bounces away at the angle of reflection
What happens when a wave is refracted?
The wave hits the boundary and slows down, bending towards the normal
What happens when a wave is diffracted?
The wave travels through a gap between two barriers and spreads out - the narrower the gap the more it spreads
How many radians is equal to 360°?
2π radians
What is phase?
The phase of a vibrating particle at a certain time is the fraction of a cycle it has completed since the start of the cycle
What is phase difference?
The phase difference between two particles vibrating at the same frequency is the fraction of a cycle between the vibrations of the two particles
What is the equation for phase difference (in radians)?
2π x distance between points (m) / wavelength (m)
2πd/λ
Define wavefront
The width of the wave, perpendicular to the direction of the wave
What are coherent waves?
Waves are coherent if they have equal frequencies and a constant phase difference
What is superposition?
Superposition is where two waves meet, interfere and create a stationary wave
What are the types of interference?
Constructive interference - where the two waves combine to make supercrests and supertroughs, this happens when the waves are in phase
Destructive interference - where the two waves cancel each other out, this happens when the waves are out of phase
What are stationary waves?
- Waves formed from the superposition of two progressive waves
- Nodes - points which don’t move, every half a wavelength between antinodes
- Antinodes - points which move the maximum displacement, every half a wavelength between nodes
- All points between two adjacent nodes are in phase to each other
Frequency in stationary and progressive waves
Stationary waves
All particles except the nodes vibrate at the same frequency
Progressive waves
All particles vibrate at the same frequency
Amplitude in stationary and progressive waves
Stationary waves
The amplitude varies from 0 at the nodes to a maximum at the antinodes
Progressive waves
The amplitude is the same for all particles
Phase difference between two particles in stationary and progressive waves
Stationary waves
Equal to mπ, where m is the number of nodes between the two particles
Progressive waves
Equal to 2πd/λ
What is the first harmonic?
The pattern of stationary waves on a string when it vibrates at its lowest possible frequency - nodes at each end of the string and an antinode in the middle
Frequency of vibrations in a string
First harmonic frequency = 1/(2 x length of string) x sqrt(tension/mass per unit length)
f = 1/2L * sqrt(T/μ)
What is a polarised wave?
A wave that oscillates in only one direction
Only transverse waves can be polarised
Polarised cameras and sunglasses use polarisation filters to reduce glare
TV and radio signals are polarised which means that the receiving aerial must be aligned in the same plane of polarisation to receive the signal at full strength
Young’s double slit experiment
A coherent light source is shined through 2 slits so that it diffracts
The two new sources of light interfere:
Where they meet out of phase they destructively interfere, making a dark fringe
Where they meet in phase they contructively interfere, making a light fringe
fringe spacing = wavelength x distance between slits and screen / slit separation
w = λD/s
Diffraction grating
A diffraction grating is a slide containing many equally spaced slits very close together
distance between slits x sin(angle between maximum and normal) = order of maximum x wavelength
dsinθ = nλ
Refractive index
A refractive index is how much a material refracts light passing through it
refractive index = speed of light in vacuum / speed of light in substance
nₛ = c/cₛ
Snell’s law
Refractive index of substance 1 x sin(angle of incidence) = refractive index of substance 2 x sin(angle of refraction)
n₁sinθ₁ = n₂sinθ₂
Critical angle
The angle of incidence when the angle of refraction is 90 so the light passes along the boundary line; any angle higher than this will not cause refraction but instead total internal reflection
sin(critical angle) = refractive index of substance 2 / refractive index of substance 1
sinθ₁ = n₂/n₁
Total internal reflection
Where the light reflects back at the boundary
Two conditions for this to happen:
The light must travel from a more optically dense to a less optically dense medium - from higher refractive index to lower refractive index
The angle of incidence of the light ray must exceed the critical angle
Optical fibres
Optical fibres make use of total internal reflection to transfer signals
They consist of:
A core made of a high refractive index material
Cladding made of a low refractive index material
Light passes through the core and the difference in refractive indexes of the core and cladding allow for total internal reflection of the light
Cladding in optical fibres
Provides tensile strength to the optical fibre - won’t break when twisted
Prevents information from transferring between different cores in a bundle
Prevents the core from being scratched - a scratch could lower the angle of incidence under the critical angle and if water gets in it could raise the refractive index above that of the core
Modal and material dispersion
Modal dispersion
Waves go off in different directions and arrive at the end at different times, having gone different distances
Reduced by having a narrower core
Material dispersion
White light is dispersed due to the speed of light in glass depending on the wavelength
Using monochromatic light prevents this from happening
