Waves Flashcards
Hader
phase of a wave
How far through a cycle the wave is
phase difference
The difference in two waves’ cycles/phases; the amount one wave lags behind another one
three units for phase difference
Degrees, radians or fractions of the wave cycle
period of a wave
The time taken for one complete wave to pass a point (i.e. the time taken for one complete oscillation of a particle about its equilibrium position)
waves in phase
Waves with the same frequency that peak together, so are an integer number of wavelengths apart e.g. if two troughs are 360 degrees away from each other
Do waves in phase need to have the same amplitude?
No - only the same frequency and wavelength need to be the same
Describe a longitudinal sound wave.
Only includes the bit I don’t tend to mention.
parallel oscillation… causes areas of compression and rarefaction
mechanical wave
A wave that needs a medium in order to transfer energy away from their source e.g. longitudinal wave
examples and non-examples of mechanical waves
Examples: sound, seismic and water waves
Non-examples: light waves/EM radiation
Longitudinal waves rely on particle oscillation, causing ____ to pass ____.
the neighbouring particle, on a vibration
Are water waves an example of longitudinal or transverse waves?
Transverse only (for the A Level) -> these are ripples
Longitudinal in terms of the water particlles - they move in circular motions
frequency
The number of oscillations per second
formulae for speed of a wave
c or v = f λ
c for EM radiation in a vacuum or vacuum-like substance e.g. air
v for other waves
polarising waves
The oscillation direction is limited to one plane (direction) i.e. all oscillations in other planes are removed
How can you use polarising filters to block out all light?
Hold two polarising filters perpendicular to each other
2 uses of polarisation
- Polaroid (glare reduction) glasses, photography
- TV aerials/radio signals
How do glare reduction glasses work?
The glasses contain polarising filters with a horizontal transmission axis.
Reflected light is partially polarised, so only the light that is vibrating in the horizontal plane can pass through the glasses (the rest of the light is blocked) which reduces the intensity of light entering the eyes.
How are polaroid filters used in TV signals?
TV signals are polarised by the orientation of the rods on the transmitting aerial.
To receive a strong signal, the receiving aerial rods need to line up with the rods on the transmitting aerial.
This is why the rods on TV aerials are all
horizontal.
Two students carried out an experiment to determine the speed of sound. This is the method used.
1. Student A stands 100 m away from Student B.
2. Student A bangs two blocks of wood together making a loud sound.
3. Student B starts a stopclock when he sees the blocks of wood bang together.
4. Student B stops the stopclock when he hears the sound and records the time.
5. The students repeat steps 2‒4 several times.
The students calculated the speed of sound from their results. Suggest the most likely source of error in the experiment
Human reaction time
Two students carried out an experiment to determine the speed of sound. This is the method used.
1. Student A stands 100 m away from Student B.
2. Student A bangs two blocks of wood together making a loud sound.
3. Student B starts a stopclock when he sees the blocks of wood bang together.
4. Student B stops the stopclock when he hears the sound and records the time.
5. The students repeat steps 2‒4 several times.
The speed of sound calculated was lower than the true speed of sound in air.
Suggest one improvement to the students’ method that would give a more accurate value for the speed of sound. Explain your answer.
Make student B stand further away, so any errors caused by student B’s reaction time is a lower proportion of the whole time; there is a lower percentage error in the recorded time.
Explain how a student could make appropriate measurements with a ripple tank and motor to determine the water wave’s wavelength.
- Measure the distance of the ripple tank with a metre ruler
- Turn the motor on and measure the time taken for 10 waves to reach the end of the ripple tank with a stopwatch
- Calculate the mean time taken
- Use v = s / t to calculate the water wave speed
- Count the number of complete waves that reach the end of the ripple tank in 10 seconds, measured with a stopwatch
- Calculate the mean frequency by dividing the number of waves by the time taken for the waves to pass
- Use λ = v / f to calculate the average wavelength
Light wave fronts are closer together/further apart in a glass block than in air. Explain why.
closer together - light travels slower in glass, because glass is denser
Imagine glass has more resistance -> light is ‘stuck there’ for longer
If a refracted ray bends away from the normal, is it travelling faster or slower than it was originally?
Faster
away
(or towards/slower)
The denser an object, the faster/slower light will travel through it.
slower
Imagine glass has more resistance -> light is ‘stuck there’ for longer
A light ray is incident on the middle of the flat side of a semicircular glass block and exits on the rounded part. In what direction does the exiting (emergent) ray go?
It maintains the same direction for the bent refracted ray - the ray is now travelling perpendicular to the glass block edge (along the normal) so doesn’t refract.
See https://i.sstatic.net/eKMye.jpg
[acccessed 19th February 2025]
How will the wavelength of a wave be affected if a wave slows down?
When would this be useful to know?
v = f λ
decreases
When drawing wave front diagrams
Describe how the radio waves reaching the car aerial produce signals in the electrical circuit of the car radio. [3]
There’s one bit I keep missing smh
- (the car aerial) absorbs radio waves or energy
- electrons are made to vibrate (in the aerial)
- creating an alternating current (in the aerial circuit)
- the (signal) frequency is the same (as the radio wave)
A ripple tank has a shallow and a deep region. Explain what happens to the waves as they pass into the deep region.
they will speed up, so wave (fronts) move further apart
displacement (formal definition)
The distance in a medium between a particle and its equilibrium position in a certain direction
oscillation (formal definition)
A displacement in one direction and then the other about the particle’s equilibrium position
What is the equilibrium position in wave motion in a medium?
The position of the medium when undisturbed by a wave
Frequency is the number of ___ ___ per second.
wave cycles
State the term describing two points on a wave with a phase difference of 0.
in phase
State the term describing two points on a wave with a phase difference of π rad.
in antiphase
progressive wave
A wave that transfers energy but not the medium through space, so its amplitude and frequency is constant
Give two examples of progressive waves.
Progressive waves can be transverse or longitudinal, so name any type of wave that is transverse or longitudinal
diffraction (+ example)
The spreading out of a wave as it passes through a small gap or around an obstacle e.g. sound from around a corner
superposition general meaning
One thing on top of another, especially similtaneously
principle of superposition
When two or more waves cross at a point, the resultant displacement (vector) equals the vector sum of the displacements of the individual waves
interference
When two waves superpose to produce a smaller/greater amplitude
constructive interference
When two waves in phase meet, if their displacements are in the same direction, the displacements combine to give a bigger displacement / amplitude
destructive interference
If two waves have opposite displacements (e.g. crest vs. trough – they are in antiphase) then they cancel each other out, so the total displacement/amplitude will be smaller
coherent waves
Waves with the same frequency and a constant phase difference i.e. one is just offset the other
incoherent waves
Waves with different frequencies and a changing phase difference
path difference
The amount by which the path travelled by one wave is longer than the path travelled by the other wave; how many wavelengths one wave is offset another
If two waves are in phase with each other, there is ____ interference.
constructive
If two waves are in antiphase with each other, there is ____ interference.
destructive
If two waves have paths of 4λ and 6λ respectively at point P, there is ____ interference at this point.
path difference = 6 - 4 = 2λ
This is an integer value, so there is constructive interference
There is constructive interference between three waves. What are their path differences like?
The path differences are integers - remember, the waves are in phase with each other.
There is destructive interference between three waves. What are their path differences like?
The path differences are integers + 0.5. Remember, the waves are in antiphase with each other.
There are three waves. The first two have a phase difference of 76, while the last one has a phase difference of 9.5 with the previous two. What would happen if a) the first and last two and b) the first two waves met at a point?
a) destructive interference (non-integer path difference)
b) constructive interference (integer path difference)
formula for path difference for constructive interference
n * λ (where n is an integer number of wave cycles)
formula for path difference for destructive interference
(n + 0.5) * λ (where n is an integer number of wave cycles)
maxima
Points when two crests or two troughs of two waves collide and reinforce one another, making the maximum possible displacement
minima
Points when a crest and a trough of two waves collide and cancel each other out, making the minimum possible displacement
What type of interference occurs at a) maxima and b) minima?
a) constructive interference
b) destructive interference
thin film interference
Don’t think you need to know, but may be in application questions?
Light waves are reflected by the two boundaries of a very thin film. They superpose and so there’s interference between them (sometimes constructive sometimes destructive) and so increasing reflection at some wavelengths and decreasing it at others
How do waves that reflect off the upper and lower boundaries of the thin film differ?
The one that reflects off the lower boundary travels further i.e. 2 * the thin film’s thickness
How do noise-cancelling earphones use interference?
They use destructive interference, generating the opposite (i.e. opposite displacement) sound waves for ambient sounds, effectively cancelling them out.
What are noise-cancelling earphones better and worse at? Why?
They are better at cancelling low frequency sounds e.g. machines, worse at human speech
Human speech is at a higher frequency, and in fact the frequency varies quite a bit
I think this is the reason, but don’t quote me
standing wave (+ alternative term)
The superposition of two progressive waves with the same frequency/wavelength and similar amplitudes, moving in opposite
directions; stationary wave
Is energy transmitted by progressive waves and stationary waves?
Progressive - yes
Stationary - no
Energy is ____ in stationary waves.
stored
How can you demonstrate standing waves?
Attach a string between two fixed points, where one end is connected to a driving oscillator
resonant frequency
A frequency on an oscillator that happens to produce an exact number of waves in the time it takes a wave to get to the other end of the string and back again, so that the original and refected
waves superpose and interfere with (reinforce) each other
A string is fixed at one end. Upon the formation of a stationary wave via reflection on this string, the wave undergoes a phase change of ____.
pi radians/180 degrees i.e. the antinodes will be 180 degrees out of phase - draw it out to convince yourself.
A stationary wave has a wavelength of 0.38 m and a frequency of 24 Hz. What is its speed?
0m/s - stationary waves don’t have a speed.
A stationary wave can be formed by two progressive waves travelling in
opposite directions. For this to happen, the two progressive waves must have…
the same frequency, wavelength and the same/similar amplitude.
At resonant frequencies, ____ of ____ fit onto the string.
an exact number, half wavelengths
How many wavelengths are there between nodes?
Half a wavelength
How many wavelengths are there between a node and an antinode?
Quarter of a wavelength
At what points are there constructive and destructive interference on a standing wave?
Node = total destructive
Antinode = constructive
This makes sense when you think about it - the progressive waves cancel each other out when the amplitude is 0
harmonic
One of many possible waves formed when a stationary wave is set up on a string with fixed nodes on either end
For a given harmonic on a guitar string, as the tension increases, the
wavelength of the harmonic…
stays constant
b) A rope has a length of 6.72 m, a mass of 3630g, and a cross-sectional area
of 3.41 cm2. What is the mass per unit length?
Give your answer to 2 s.f.
3.630kg
3.630/6.72 = 0.540…~0.54kg/m
The area/volume of the string doesn’t matter here.
The harmonic number is the number of ____.
Just for understanding/ease
antinodes
Number of nodes on a harmonic = ?
Number of antinodes (OR harmonic number) + 1
The third harmonic has ____ times the frequency of the first harmonic.
three
How many wavelengths are there at the 11th harmonic?
11th harmonic = 11 * 0.5 (or 5.5) wavelengths
What is the size of the wavelength of the third harmonic?
3 antinodes -> whole length is 3/2 (1.5) wavelengths
Therefore one wavelength = length of string / (3/2) = (2 * length of string) / 3
What is the frequency at a node?
0Hz
Compare the speed in progressive and stationary waves.
Progressive: wave speed = speed the wave travels through the medium
Stationary: each point on wave oscillates at a different speed BUT the overall wave doesn’t move
Nodes on a standing wave move. True or false?
False - they are stationary
f0 = ?
first harmonic
sometimes this is f1
notation for the third harmonic
f3 (I think if you start at f0 for the fundamental frequency then it would be f2)
Compare the phase and frequency of progressive and standing waves.
The phase varies along progressive waves i.e. between 0° and 360°, but all the points between two nodes on a standing wave are in phase because the two progressive waves that it is made of superpose
The frequency/wavelength of a standing wave is the same as the travelling (progressive) waves that form it
speed in a stationary wave
Every point on a stationary wave oscillates at a different speed, however the overall wave doesn’t move
Compare the amplitude of progressive and standing waves.
Amplitude is the same for all points in a progressive wave (in turn, as it goes along) whereas the amplitude is different for each point depending on the amount of superposition (i.e. total destructive interference, or the amount of destructive/constructive interference)
Points equidistant to a node that are on either side of the node have ____ displacements as they are oscillating ____.
opposite, out of phase
All points between adjacent nodes are displaced in ____ direction(s) as they are oscillating in ____.
the same, phase - this is because on a stationary wave, these points represent constructive interference ?
Points either side of a node are ____.
out of phase
interactions of waves with matter (4)
- Reflection
- Refraction
- Diffraction
- Absorption
When do stationary waves form?
When the time it takes for a wave to travel along a string and back = integer number of oscillations -> this causes the reflected wave to superpose (strengthen) the new wave
Describe how you can use microwaves to determine the fundamanetal frequency.
Send a microwave beam at a metal
plate - the wave and reflection can superpose to produce a stationary wave.
Move a probe between the transmitter and reflecting plate to find the nodes and antinodes; the meter connected to the probe receives no signal at the nodes (no displacement) and the maximum signal at the antinodes (max displacement).
Describe how you can determine the fundamanetal frequency of sound waves.
Use a loudspeaker to produce stationary sound waves in a closed glass tube (the sound waves reflect off the end of the tube).
There is powder placed all along the bottom of the tube. This power is shaken
away from the antinodes but left undisturbed (i.e. piles form) at the nodes.
The longer the string, the ____ the resonant frequency. Explain your answer.
lower
the half-wavelength is longer (c = fl, so if l increases, f decreases for a fixed c).
The heavier the string, the ____ the resonant frequency. Explain your answer.
lower
because waves travel more slowly down the string - for a given length, a lower velocity makes a lower frequency (v = fλ).
The lower the tension on the string, the ____ the resonant frequency. Explain your answer.
lower
because waves travel more slowly down a loose string - for a given length, a lower velocity makes a lower frequency (v = fλ).
Refraction is due to the ____ changing when a wave enters a new ____ with a different ____ ____.
speed, medium, optical density
Wavefronts are lines drawn to represent the ____ of a wave.
peaks
When a wave is refracted, how do the speed, frequency and wavelength change?
The wave’s speed and wavelength change but its frequency remains constant.
(consider the formula v = f λ
refractive index (incl. symbol units)
How optically dense a material/medium is
symbol = n
no units
refractive index of air
1
The greater the difference in n between two media, the ____ the change in speed and so the ____ the light refracts.
greater, more
absolute refractive index
The ratio between the
speed of light in a vacuum (c) and and the speed of light in that material (cs)
n = c / cs
For a ray leaving a glass block, what must you do when using the formula for Snell’s Law?
The angle of incidence must be substituted in as the angle of refraction and the angle of refraction must be inputted as the angle of incidence
i.e. n = sin (i) / sin(r) becomes n = sin(‘refracted ray’ in glass block) / sin(‘incident ray’ that’s left the glass block)
Diffraction is most prominent when ____.
the width of the gap is similar to the wavelength
The bigger the gap is than the wavelength, the ____ the resulting diffraction.
smaller
The greater the wavelength, the ____ the diffraction.
greater
Where the gaps are much, much smaller than the wavelength of the wave, ____ occurs. Explain why.
no diffraction - basically all the waves are reflected (very few waves are transmitted)
Where the gaps are much, much bigger than the wavelength of the wave, ____ occurs. Explain why.
no diffraction - diffraction is negligible
A wave travels through a gap with a width similar to its wavelength. Compare the amounts of diffraction if the wavelength is bigger than the gap and if the wavelength is smaller than the gap.
More diffraction occurs (i.e. the wave spreads out more) when the wavelength is bigger than the gap than if the wavelength is smaller than the gap.
What does more diffraction look like? Visualise it.
Waves that curl more at the ends i.e. a WiFi symbol compared to the locus of a square or slight smile
What changes when a wave passes through a small gap? Explain why.
Wavelength stays the same, but the amplitude decreases because both sides of the boundary absorbed some of the wave’s energy.
monochromatic light
Electromagnetic radiation of a certain wavelength
How can you produce monochromatic light?
e.g. using a ray box (i.e. lasers/LEDs/some filters)
How does light refract on a glass triangular prism?
Light passes into the triangular prism at an angle to the normal
The light bends towards the normal (smaller gradient) - doesn’t have to be horizontal
The light reaches the other end of the prism and refracts again, but this time away from the normal (at the same angle as the incident ray?)
https://www.youtube.com/watch?v=UCiu2IA4Lmg
Note I think the first and final ray lines here should be identical I think (don’t quote me)
total internal reflection
When a waves reaches a boundary between two media, and instead of being refracted, they are completely reflected back into the first medium
A progressive wave travels to the right along a rope in the direction M to N, which are found at the equilibrium position (the wave is going up, then down and then up again).
X marks a point on the rope at the end of the first wavelength.
The wave has a frequency of 5.0 Hz, a wavelength of 1.0 m and an amplitude of 0.20 m.
Where will X be after 0.15s? (Give magnitude and direction of the position)
Struggled 22/2/25
above MN by 0.20 m
T = 1/f = 0.2s
0.15 = 3/4 of 0.2 thus X will be 3/4 wavelengths along from the starting position
The wave moves, not the point on the rope, so draw the wave translated 3/4 wavelength along.
The point on the wave above/below point X is the new position - this is the maximum displacement of the wave above the equilibrium position
For a stationary wave, what do the terms ‘in phase’ and ‘antiphase’ mean?
In phase - two points are displaced on the same side of the equilibrium position
Antiphase = out of phase = opposite displacement; on the opposite sides of the equilibrium position = 180°/2π out of phase (same everywhere)
A string is stretched between two fixed points O and R which are 120 cm apart.
P and Q are points on the string.
OP = 30 cm
OQ = 90 cm
At a certain frequency the string vibrates at its first harmonic. P and Q oscillate in phase.
The frequency is gradually increased.
What is the next harmonic at which P and Q will oscillate in phase?
Third harmonic - just draw out sketches of the harmonics.
The points will be in phase whenever they are on the same side of the equilibrium position.
When a wave refracts away from the normal, how do the following change?
a) speed
b) frequency
c) velocity
d) amplitude
e) wavelength
a) decreases
b) doesn’t change
c) decreases (incl. direction)
d) doesn’t change if there’s ONLY refraction in any direction (decreases if there’s some reflection & refraction simultaneously)
e) decreases (v = f lambda)
Explain how the amplitude of a light wave changes when a ray reaches the boundary between air and glass, with an angle of incidence of the critical angle.
Refraction occurs along the boundary (angle of refraction = 90 degrees)
Amplitude decreases because some energy is lost from the refraction
formula to link the refractive indices of two media and the wavelengths of light that pass through them
not in FB, but not sure you need to know
n1 / n2 = λ2 / λ1
formula to link the refractive indices of two media and the speeds of light that pass through them
don’t think you need to know
n1 / n2 = v2 / v1
Derive the formula to link the refractive indices of two media and the wavelengths of light that pass through them
not in FB, but not sure you need to know
n1 = c / v1
n2 = c / v2
Rearrange to make v the subjects (don’t have to do, just makes simplifying a bit easier):
v1 = c / n1
v2 = c / n2
v1 / v2 = (c / n1) / (c / n2)
= cn2 / cn1
= n2 / n1
Using v = fλ (f is constant):
fλ1 / fλ2
= λ1 / λ2
Therefore n2 / n1 = λ1 / λ2 as required
Derive the formula to link the refractive indices of two media and the speeds of light that pass through them
don’t think you need to know
n1 = c / v1
n2 = c / v2
n1 / n2 = (c / v1) / (c / v2)
= c v2/ c v1
= v2 / v1 as required
What exactly is Snell’s Law?
A formula that relates the angle of incidence to the angle of refraction at a boundary between two media
In words: the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for two media (and light of a given colour)
In formula form: n1 * sini = n2 * sinr
i and r can be replaced by 1 (first material) and 2 (second material) respectively
(in FB)
Why do different wavelengths (e.g. colours in a rainbow) travel at different speeds in a glass prism?
Glass has different refractive indices for different wavelengths of light.
i.e. red light travels fastest and so deviates (refracts) less.
ig this links to TIR in fibre optic cables.
When does TIR occur?
When a light ray meets the boundary from a medium with a higher refractive index to another medium with a lower refractive index.
critical angle
The minimum angle of incidence which causes a ray (at the boundary between a medium with a higher refractive index to one with a lower refractive index) to refract perpendicular to the normal/reflect back towards the first substance.
The critical angle needs to be ____ for total internal reflection to occur
exceeded
