Chapter 4 - Waves Flashcards
What are mechanical waves?
- Waves that pass through a substance
- Cannot travel through a vacuum
- e.g. sound waves, seismic waves, waves on a string
What are mechanical waves made up of?
Vibrations passing through the substance
How are sound waves in air created?
By making a surface vibrate so it sends compression waves through the surrounding air
What are electromagnetic waves?
- Oscillating electric and magnetic fields that progress through space without the need for a substance
- Can travel through a vacuum
- A vibrating electric field generates a vibrating magnetic field, which generates a vibrating electric field further away, and so on
What are longitudinal waves?
Waves in which the direction of vibration of the particles is parallel to (along) the direction of energy transfer/direction in which the wave travels
Examples of longitudinal waves
Sound waves, primary seismic waves, compression waves along a spring
What are compressions of a longitudinal wave?
Areas of high pressure - particles closer together
What are rarefactions of a longitudinal waves?
Areas of low pressure - particles further apart
What are transverse waves?
Waves in which the direction of vibration is perpendicular to the direction of travel/energy transfer
Examples of transverse waves?
Electromagnetic waves, Secondary seismic waves, waves on a string
When are transverse waves plane-polarised?
When vibrations stay in one plane (direction) only
When are transverse waves unpolarised?
- When vibrations change from one plane (direction) to another
- Can vibrate in all directions perpendicular to the direction of propogation (travel)
Why can longitudinal waves not be polarised?
- Particles only vibrate in the same direction that the wave travels
- Can only travel in one plane, so we do not refer to them as being polarised or unpolarised
How do transverse waves become polarised?
- Unpolarised waves travel through a polariser (e.g. a polaroid filter for light), which only lets vibrations in a certain direction through, according to the alignment of its molecules
- Polariser blocks waves of other planes/polarisations so they cannot pass through
What happens when light passes through two polaroid filters at 0°/180°/360° to each other
Light intensity at a maximum (that it can be when polarised, but less than if the light was unpolarised)
What happens when a second polaroid filter is rotated from being in alignment with a first filter to being at 90° to it
- Light intensity reduces from a maximum as the second filter is rotated
- Intensity at a minimum when the second filter reaches 90°
- First filter polarises light in one plane, second filter polarises light at a right angle to this plane, so now a minimum amount can pass through
What happens when a second polaroid filter is rotated form being at 90° to a first filter to being in alignment with it
- Light intensity increases from a minimum as the second filter is rotated
- Intensity at a maximum when the second filter is aligned wioth the first
- Both filters polarising the light in the same plane, so second filter has no overall effect on intensity and it remains at a maximum
What is the plane of polarisation of an electromagnetic wave?
The direction in which the electric field oscillates
What effect do polaroid sunglasses have on light?
- Reduce the glare of light reflecting off of water or glass
- Reflected light is polarised and intensity reduced when it passes through the polaroid sunglasses
What is the displacement of a wave/vibrating particle?
Its distance and direction from its equilibrium position
What is the amplitude of a wave?
The maximum displacement of a vibrating particle:
- Height or depth of a transverse wave from its equilibrium position
- Distance between particles in areas of compression (the denser the compression, the higher the amplitude)
What is the wavelength of a wave?
The least distance between two adjacent vibrating particles with the same displacement and velocity at the same time
- Distance between adjacent crests of a transverse wave
- Distance between adjacent compressions of a longitudinal wave
What is one complete cycle of a wave?
Motion of a wave from one maximum displacement to the next maximum displacement
- From one wave peak to the next
- Wavelength is the distance of one complete cycle
What is the period of a wave?
The time for one complete wave to pass a fixed point
What is the frequency of a wave?
- The number of complete waves passing a point per second
- The number of cycles of vibration of a particle per second
Period equation
Period = 1/frequency
What is the relationship between frequency and wavelength?
- Wavelength and frequency are inversely proportional
- The higher the frequency of a wave, the shorter its lenght, and vice versa
Wavespeed equation
Wavespeed, c = fλ
- Each wave crest travels a distance equal to one wavelength, λ, in the time taken for one cycle
- The time taken for one cycle = 1/f
- Therefore wavespeed = distance travelled/time taken = λ/1/f = λf
What is the definition of the phase of a particle?
The phase of a vibrating particle at a certain time is the fraction of a cycle it has completed since the start of a cycle
What is the phase difference of two particles?
Phase difference between two vibrating particles at the same frequency is the fraction of a cycle between the vibrations of the two cycles
- Measured in either degrees or radians, where 1 cycle = 360° = 2π radians
How can different properties of waves be observed?
Using a ripple tank - a shallow transparent tray of water with sloping sides
Why are the sides of a ripple tank sloped?
- To prevent waves reflecting off the sides of the tank
- If they did reflect, it would be difficult to see the waves
How does a ripple tank work?
- A pattern of wavefronts of constant phase difference (e.g. crests) are cast on the floor
- The direction in which the wave travels is at roght angles to the wavefront
Why can wavefronts be observed on the screen of a ripple tank?
- Each wave crest acts like a convex lens and concentrates the light onto the screen so the pattern on the screen shows the wave crests
What is reflection?
When straight waves are directed at a certain angle to a hard flat surface (the reflector), and reflected off at the same angle
Relationship between the angles of the reflected and incident rays to the normal
- The angle between the reflected wavefront and the surface is the same as the angle between the incident wavefront and the surface
- The direction of the reflected wave is at the same angle to the reflector as the direction of the incident wave
- Effect observed when the light ray is directed at a plane mirror
What is refraction?
- When waves pass across a boundary causing the wavespeed and wavelength to change
- If the wavefronts approach at an angle to the boundary, they change direction as well as speed
Effect of refraction on a wave when passing from a more dense to a less dense material
E.g. a light wave travelling from from glass to air:
- Wave travels more slowly in glass than in air
- Wavelength smaller as it’s travelling slower
- Wavelength shortening while crossing at an angle causes wave to change direction and bend away from the normal
What is diffraction?
- Occurs when waves spread out after passing through a gap or round an obstacle
How does the width of the gap affect the amount of diffraction?
The narrower the gap, the more the waves spread out
How does wavelength affect the amount of diffraction?
The longer the wavelength, the more the waves spread out
Why does diffraction happen?
- Consider each point on a wavefront as a secondary emitter of wavelets
- The wavelets travel only in the direction that the wave is travelling, not in the reverse direction
- Wavelets combine to form a new wavefront spreading beyonf the gap
Equation for phase difference
The phase difference in radians = 2πd/λ
Why does a bigger satellite dish need to be aligned more carefully than a smaller one
- Satellite TV dishes in Europe must face south as satellites orbit the Earth above the equator
- The bigger the dish the stronger the signal it can receive
- A bigger dish means more radio waves are reflected by the dish onto the aerial
- But a bigger dish reflects the waves to a smaller focus because it diffracts the waves less
- The dish therefore needs to be aligned more carefully than a smaller one, otherwise it will not focus the radio waves onto the aerial
Definition of superposititon
When two waves meet, the total displacement at a point is equal to the sum of the individual displacements at that point
Effect of superposition when a crest meets a crest
- A supercrest is created
- The two waves reinforce each other
Effect of superposition when a trough meets a trough
- A supertrough is created
- The two waves reinforce each other
Effect of superposition when a crest meets a trough
- The resultant displacement is zero
- Waves cancel each other out
- If they are not at the same amplitude, the resultant is a minimum
Examples of superposition
- Stationary waves on a rope
- Water waves in a ripple tank
Superposition of stationary waves on a rope
- Two progressive waves of the same frequency sent continuously along a rope from either end
- Waves superpose at fixed points to form nodes
What is a node on a stationary wave?
- Points of no displacement
- At each node, the two sets of waves are always 180° out of phase, so they cancel each other out
What are coherent waves?
- Waves vibrating with the same frequency with a constant phase difference
How are nodes formed on a stationary wave?
- At each node, the two sets of waves are always 180° out of phase, so they cancel each other out through superposition
What is a progressive wave?
A wave which travels continuosly in a medium in the same direction without a change in its amplitude
Superposition of water waves in a ripple tank
- A vibrating dipper on a water surface sends out circular waves
- Points of cancellation (constructive interference) when a crest from one dipper meets a trough from the other - seen as gaps in the wavefronts
- Points of reinforcement (destructive interference) where a crest from one dipper meets a crest from the other, or a trough from one dipper meets a trough from the other
What is interference?
- Waves continuously pass through each other at constant frequency and phase difference - waves are coherent
- Cancellation and reinforcement happen at fixed positions
What is constructive interference?
- When two waves are travelling in the same direction and in phase with each other
- Superposition occurs and the amplitude of the resultant wave is the sum of the individual waves
What is destructive interference?
- When two waves are travelling in the same direction and 180° out of phase
- Superposition occurs and the two amplitudes cancel each other out
What would be the effect on interference if the phase difference of the two waves changed at random?
- Points of cancellation and reinforcement (interference) would move about at random
- Therefore no interference pattern would be seen
How can a microwave transmitter be used to show that microwaves become weaker as they travel?
- Place a receiver in the path of a microwave beam from the transmitter
- Move the receiver gradually away from the transmitter
- The receiver signal decreases with distance from the transmitter, so microwaves become weaker as they move away from the transmitter
How can a microwave transmitter be used to show that microwaves cannot pass through metal?
- Place a metal plate in between a microwave transmitter and the receiver
- Receiver will have no signal, so microwaves cannot pass through the metal
How can a microwave transmitter be used to show that microwaves diffract?
- Use two metal plates to make a narrow slit in the path of the microwave beam, between the transmitter and receiver
- Move the receiver in a curve/semicircle
- Reading drops when close to the plates at either end
- Reading increases when moved towards the centre of the curve parallel to the gap
- Keep reader in fixed position and widen the gap to see the reading drop as the waves diffract less
How can a microwave transmitter be used to show that microwaves interfere?
- Use two metal plates to make a pair of slits in the path of the microwave beam, between the transmitter and receiver
- Move the receiver along the metal plates from a distance to find points of maxima and minima where constructive and destructive interference has taken place
What is the first harmonic/fundamental mode of vibration?
- A stationary wave of a single loop with a node at either end (two in total)
What is an antinode?
- The point with maximum amplitude halfway between two nodes
Equation for the distance between adjacent nodes
Distance between adjacent nodes = 1/2λ
When is the second harmonic formed?
- When the frequency is twice as high as it is to form the first harmonic, corresponding to half the previous wavelength
- Lenght of the rope now one full wavelength
- Frequency at each harmonic is an integer multiple of the frequency at the first harmonic
How do stationary waves vibrating freely not transfer energy to surroundings?
- Amplitude of vibration is zero at the nodes so there is no energy
- Amplitude of vibration is maximum at the antinodes, so there is maximum energy
- Nodes and antinodes at fixed positions, so no energy is transferred in a freely vibrating stationary wave pattern
How do stationary waves form?
Two progressive waves pass through each other with the same frequency
- Usuall one progressive wave and its reflection
Cycle of a stationary wave
- When in phase, they interfere constructively and produce a larger wave
- 1/4 of a cycle later, the waves have moved 1/4λ in opposite directions so are now in antiphase and interfere destructively to cancel each other out
- A further 1/4 cycle later, they are in phase again so interfere constructively, but reversed (i.e. if first was two crests meeting, it is now two troughs meeting)
Position of nodes
Nodes in fixed posititons with the stationary wave oscillating between them
When is the phase difference between two vibrating particles on a stationary wave zero?
When the two particles are between adjacent nodes or separated by an even number of nodes
When is the phase difference between two vibrating particles on a stationary wave 180°/π
When the two particles are separated by an odd number of nodes
How does the frequency of vibrating particles in a stationary wave vary?
All particles except those at nodes vibrate at the same frequency
How does the frequency of vibrating particles in a progressive wave vary?
All particles vibrate at the same frequency
How does the amplitude of vibrating particles in a stationary wave vary?
Varies from zero at the nodes to a maximum at the antinodes
How does the amplitude of vibrating particles in a progressive wave vary?
Amplitude the same for all particles
How does the phase difference between two particles in a stationary wave vary?
Equal to mπ, where m is the number of nodes between the particles
How does the phase difference between two particles in a progressive wave vary?
Equal to 2πd/λ
How can a microwave transmitter be used to show a stationary wave?
- Direct microwaves from a transmitter normally at a metal plate
- Metal plate reflects microwaves back at the transmitter, which form a stationary wave with waves from the transmitter
- Move the detector along the line between the transmitter and the metal plate
- Detector signal zero or a minimum at equally spaced positions along the line where nodes occur, spaced out at intervals of half a wavelength
Displacement when two troughs meet
Superpose to produce a maximum negative displacement, not a minimum
Controlled arrangement to produce stationary waves (required practical)
- Tie one end of a string to a mechanical vibrator connected to a frequency generator
- Pass the other end of the string over a pulley, supported by a weight which keeps tension constant
- Increase the frequency on the generator to produce different patterns of stationary waves
When is the first harmonic pattern of vibration seen?
At the lowest possible frequency that gives a pattern
- Length, L = 1/2λ1, so λ1 = 2L
- Therefore first harmonic frequency, f = c/λ1 = c/2L
When is the second harmonic seen?
- Node in the middle with 2 loops, so string has 2 loops
- Wavelength of the stationary wave, λ2 = L as each loop is 1/2λ
- Therefore equation for frequency of the second harmonic, f2 = c/λ2 = c/L = 2f1
At what frequencies do stationary wave patterns appear?
nf1, where n is the nth harmonic
How do stationary waves form?
- A progressive wave is sent out by a vibrator
- The crest reverses its phase when it reflects at the fixed end and travels back as a trough
- When reaching the vibrator, it reflects and reverses phase again, travelling away as a crest
- This is reinforced by a new crest from the vibrator so the amplitude increases
Conditions for a stationary wave to form
- The time taken for a wave to travel along the string and back should be equal to the time taken for a whole number of cycles of the vibrator
- Time taken for wave to travel along string and back = 2L/c
- Time taken for vibrator to pass through a whole number of cycles = m/f, where m is an integer
2L/c = m/f
L = mλ/2 = a whole number of half wavelengths
What does the pitch of a note correspond to?
Frequency
How can the pitch of the note from a stretched string be altered?
By changing the tension or altering the length of the string
How can the pitch of the note from a stretched string be increased?
Raising the tension or shortening the length
How can the pitch of the note from a stretched string be decreased?
Lowering the tension or increasing the length
Equation linking frequency and tension
4f = 1/2l√T/μ
- f = first harmonic frequency
- T = tension
- µ = mass per unit length
How to use a tuning fork to tune a vibrating string
- By changing the length or altering tension
- Sound from vibrating string includes all harmonic frequencies, tuning fork vibrates only at a single frequency
- Wire tuned when its first harmonic frequency is the same as the tuning fork frequency
How to check is a wire is tuned?
- Balance a small piece of paper on the wire at its centre
- Place the vibrating tuning fork at one end of the wire
- Paper will fall off the wire if it is tuned correctly
How does an oscilloscope work?
- A filament emits electrons in a beam into an electron tube towards a flourescent screen at the other end of the tube
- Light is emitted from the spot on the screen where the beam hits the screen
How is the spot on an oscilloscope screen moved?
Affected by pd across either pair of deflecting plates:
- no pd across either and spot stays in same position
- deflected vertically if pd is applied across the Y-plates
- deflected horizontally if pd is applied across the X-plates
- Displacement proportional to applied pd in both cases
What are the X-plates of an oscilloscope used for?
- X-plates connected to time base circuit
- Makes spot move at constant speed left to right across the screen, then back again much faster
- As spot moved at a constant speed, the x-scale can be calibrated, usually in milliseconds or microsecond per cm
What are the Y-plates of an oscilloscope used for?
- Pd to be displayed connected to Y-plates via the Y-input
- Spot moves up and down as it moves left to right
- Traces out waveform on screen
- Vertical displacement of spot proportional to pd applied to the Y-plates, so Y-input calibrated in volts per cm
How to measure peak pd from an oscilloscope
- Measure the amplitude of the waveform from the y-axis
- Multiply amplitude by set value of the Y-gain from the dial
How to measure frequency of the alternating pd from an oscilloscope
- Measure the distance for one full cycle horziontally across the x-axis
- Multiply distance for one full cycle by set time base from the dial to find time period (time for one full cycle)
- frequency = 1/T
