4.4 - Waves Flashcards
What is a wave?
The transfer of energy (not matter)
They are formed when a source produces a disturbance eg:
• a continuous vibration
• sudden single movement
• a pulse
What is a progressive wave?
- an oscillation that travels through matter or vacuum
* transfers energy from one place to another, but does not transfer matter
What happens to particles in a medium when a progressive wave passes through?
- they move from their equilibrium position to a new position
- the particles exert forces on each other
- a displaced particle experiences a restoring force from its neighbours and is pulled back to its original position
What are transverse waves?
Oscillations of particles are perpendicular to the direction of energy transfer
Peaks and troughs are where the oscillating particles are at a maximum displacement from their equilibrium position
Eg:
• waves on surface of water
• EM waves
• S-waves from earthquakes
What are longitudinal waves?
Oscillations of particles are parallel to the direction of energy transfer.
Compressions and rarefactions are formed when they travel through a medium
Eg:
• sound waves
• P-waves from earthquakes
What is displacement?
Distance any part of a wave has moved from the equilibrium position in a particular direction
A vector, so can have a positive or negative direction
Symbol = s Unit = metres (m)
What is amplitude?
The maximum displacement from equilibrium
Can be positive or negative
Symbol = A Unit = metres (m)
What is wavelength?
Minimum distance between 2 points in phase on adjacent waves
Eg from peak to peak, compression to compression
Symbol = λ Unit = metres (m)
What is a time period?
Aka period of oscillation
The time taken for one oscillation/one wave to move one whole wavelength pasta given point
Symbol = T Unit = seconds (s)
What is frequency?
The number of oscillations per unit time at any point
Symbol = f Unit = Hz
What is wave speed?
Distance travelled by the wave per unit time
Symbol = v (c is light) Unit = metres per second (ms^-1)
What is phase difference?
The fraction of a cycle between waves/oscillations of points on a wave
Measures in degrees/radians
1 wavelength = 360º or 2π radians
What is the wave equation?
v = fλ
v = wavespeed f = frequency λ = wavelength
How is the wave equation derived?
v = s/t
From the definition of a period, in 1 second:
t = T
s = 1λ
v = λ/T
T = 1/f
v = fλ
What is the relationship between period and frequency?
f = 1/T
Frequency is the inverse of period
What is a wave profile?
A graph showing the displacement of the particles in a wave against the distance along the wave
What does it mean if particles are in phase?
- when particles are oscillating perfectly in step with each other
- eg they both reach their maximum positive displacement at the same time
- they have a phase difference of a multiple of 2π (0, 2π, 4π etc)
- can have different amplitudes, but must have the same frequency
What does antiphase mean?
Particles oscillating completely out of step with each other (one reaches its maximum positive displacement when the other reaches its maximum negative displacement)
Have a phase difference multiples of π (π, 3π, 5π etc)
What is path difference?
The difference in the distance travelled by two waves from the source to a specific point
Measured in metres or fractions of a wavelength
On a wave profile, what value does the distance between 2 peaks represent?
Wavelength (λ)
Can also be measured using a trough and a trough, or any point and its corresponding point on another wave
On a displacement-time graph, what value does the maximum displacement represent?
Amplitude (A)
Upwards = positive displacement, downwards = negative displacement
On a graph with time on the x-axis and displacement on the y-axis, what value does the distance between 2 peaks represent?
The time period (T)
What is reflection?
The change in direction of a wave at a boundary between 2 different media, so that the wave remains in the original medium.
Eg light reflecting off a mirrored surface
What is the law of reflection?
The angle of incidence is equal to the angle of reflection.
Note: angles are measured from the normal
What effect does reflection have on the wavelength and frequency of a wave?
No effect - the stay the same
What is refraction?
The change in direction of a wave as it changes speed when it passes from one medium to another (of different density)
How does speed affect how a wave refracts?
- if a wave speeds up, it’ll refract AWAY from the normal
* if a wave slows down, it’ll refract TOWARDS the normal
How do light and sound waves refract?
LIGHT
• when entering a denser medium, EM waves slow down and refract towards the normal
• when entering a less dense medium, EM waves speed up and refract away from the normal
SOUND
• when entering a denser medium, sound waves speed up and refract away the normal
• when entering a less dense medium, sound waves slow down and refract towards the normal
What effect does reflection have on the wavelength and frequency of a wave?
• frequency remains the same
- if the wave slows down, wavelength becomes shorter
- if the wave speeds up, wavelength becomes longer
What is diffraction?
The phenomenon in which waves passing through a gap or around an obstacle spread out.
What effect does diffraction have on the properties of a wave?
No effect - speed, frequency and wavelength all remain the same
How much does a wave diffract by?
- it depends on the relative sizes of the wavelength and the gap/obstacle
- diffraction effects become most significant when the size of the gap/obstacle is around the same as the wavelength
What is polarisation?
The phenomenon in which a transverse wave only has oscillations in one direction
What does unpolarised mean?
When oscillations of a transverse wave occur in many different directions
What does plane polarised mean?
When oscillations of a transverse wave are limited to only one plane
What does partially polarised mean?
When there are more oscillations of a transverse wave in one particular plane, but the wave is not completely plane polarised
Occurs when transverse waves reflect off a surface
What is intensity?
Intensity of a progressive wave is the radiant power passing through a surface per unit area
Units watts per square metre (Wm^2)
What is the relationship between intensity and distance from a light source?
I ∝ 1/r²
I = intensity r = radius
What is the equation for intensity?
Intensity = power/area
What is the relationship between intensity and amplitude?
Intensity ∝ amplitude²
What is an electromagnetic wave?
- a transverse wave
- when electric and magnetic fields oscillate at right angles to each other
- can travel through a vacuum
What are the wavelengths of different types of EM radiation?
Gamma rays: <10^-16m to 10^-10m
X-rays: 10^-13m to 10^-8m
UV: 10^-8m to 4x10^-7m
Visible: 4x10^7m to 7x10^-7m
Infrared: 7x10^-7m to 10^-3m
Microwaves: 10^-3m to 10^-1m
Radiowaves: 10^-1m to >10^6 m
How can you distinguish between X-rays and gamma rays?
X-rays are emitted by fast-moving electrons
Gamma rays are emitted from unstable nuclei
What are the properties of electromagnetic waves?
They can be: • reflected • refracted • diffracted • plane polarised
They can travel through a vacuum
All EM travel through a vacuum at 3x10^8 metres per second, which is approximately the speed of EM waves in air
How can unpolarised EM waves be polarised?
- polarising filters for light
* metal grilles for microwaves?
What are polarisers?
Filters that polarise EM waves
The nature of the polariser depends on the part of the EM spectrum to be polarised
All polarisers only let waves with a particulate orientation through
What are polarising filters?
- polarises light
- they are plastic films that contain very long crystals, which polarise light
- they are used in sunglasses and over liquid crystal displays eg watches
What happens when you place 2 polarising filters together and rotate them?
- unpolarised light passing through the first filter is plane polarised
- if the second polarising filters (sometimes called analyser) is in the same plane as the first, the plane polarised light passing through is unaffected.
- if the second Polaroid is slowly rotated, the intensity of light transmitted drops.
- when the second filter has turned 90º, no light is transmitted,titled and the intensity falls to 0.
Howe do metal grilles polarise microwaves?
same way as polarising filters - they only allow microwaves through which oscillate in a particular plane
How can microwaves and metal grilles be used to demonstrate polarisation?
Place a metal grille between a source of plane polarised microwaves and a receiver
Rotate the metal grille through 180º, around the axis of the beam
Note the intensity of microwaves recorded by the receiver
What is the refractive index?
- a property of a material
- tells you how much a material refracts light
- the greater the refractive index, the more light is refracted towards the normal when it enters.
Calculated by n=c/v
n = refractive index c = speed of light in a vacuum v = speed of light through the material
What is the refraction law?
at a boundary:
n sinθ = k
n = refractive index of the material θ = angle between the normal and the incident ray k = a constant
What is Snell’s Law?
Describes what happens when light travels from one medium to another
n1 sinθ1 = n2 sinθ2
n1 = refractive index of original medium sinθ1 = angle of ray in original medium
n2 = refractive index of second medium sinθ2 = angle of ray in second medium
What is total internal reflection?
The reflection of all light hitting a boundary between 2 media back into the original medium
Conditions:
• the light must originally be travelling through a medium with a higher refractive index than the other medium at the boundary
• the incidence angle at the boundary must be greater than the critical angle
What is the critical angle?
The angle of incidence at the boundary between 2 media that will produce an angle of refraction of 90º
How can you derive the equation for the critical angle when light moves through a medium into air?
At the critical angle C, θ(air)= 90º
Using Snell’s law:
n1sinC= n(air)sin90º
sin90 and n(air) = 1
nsinC = 1
sinC = 1/n
What is superposition?
Overlap of 2 waves at a point in space
What is the principle of superposition of waves?
When 2 waves meet at a point, the resultant displacement at that point is equal to the sum of displacements of the individual waves
What is interference?
Superposition of 2 progressive waves from coherent sources to produce a resultant wave with a displacement equal to the sum of the individual displacements from the 2 waves
What is constructive interference?
Superposition of 2 waves in phase so that the resultant wave has a greater amplitude than the original waves
Since intensity ∝ amplitude², the increased amplitude results in increased intensity
What is destructive interference?
- Superposition of 2 waves in antiphase so that the waves cancel each other out and the resultant wave has a smaller amplitude than the original waves
- If the 2 waves have the same amplitude, the resultant wave will have 0 amplitude and therefore 0 intensity
What is an interference pattern?
A pattern of constructive and destructive interference formed as waves overlap
What is coherence?
When waves emitted from 2 wave sources have a constant phase difference
This means the waves must also have the same frequency
What is path difference?
The difference on the distance travelled by 2 waves from the source to a specific point
Measured in wavelengths (λ) or metres (m)
What are maxima?
Points of greatest amplitude in an interference pattern, produced by constructive interference
Occurs when:
• waves meet in phase
• path difference is a multiple of λ
What are minima?
Points of the least amplitude in an interference pattern, produced by destructive interference
Occurs when:
• waves meet in antiphase
• path difference is an odd number of half wavelengths, (n+1/2)λ
Interference with sound
- 2 loudspeakers connected to the same signal generator will emit coherent sound waves
- the interference pattern consists of a series of maxima (loud areas) and minima (quiet areas)
- maxima and minima can be detected by ear or by microphone
Interference with microwaves
- producing coherent sources of microwaves can be difficult, so a single source is used with a double slit
- the microwaves diffract, and then overlap to form an interference pattern which can be detected with a microwave receiver connected to an oscilloscope or voltmeter
Describe Young’s Double slit experiment
- he used a monochromatic source of light (which can be achieved by using a colour filter which only allows a specific frequency of light through)
- the light passes through a narrow single slit to diffract the light.
- light diffracting from the single slit reaches the double slit in phase. It then diffracts again from the double slit
- each slit acts as a source of coherent waves, which spread from each slit, overlapping and forming an interference pattern due to constructive and destructive interference
- the interference pattern can be seen on a screen as alternating bright and dark fringes
What does Young’s double-slit experiment prove?
That light is a wave
How can you work out the wavelength of a wave producing an interference pattern from 2 coherent sources?
λ = ax/D
λ = wavelength a = distance between slits/ coherent sources x = distance between 2 maxima D = distance from source to screen
NOTE: this equation only works when a «_space;D
What is a stationary wave?
- aka standing wave
- a wave that remains in a constant position with no net transfer of energy
- characterised by nodes and antinodes
How do stationary waves form?
- a progressive wave is produced and reflected
- the reflected wave interferes with the incident wave
- this produces a resultant wave with nodes where there is destructive interference and antinodes where there is constructive interference
What are the conditions for the production of stationary waves?
- the wave generator must produce a whole number of waves in the time it takes for the wave to get to the end and back again
- the waves must have the same wavelength and frequency
What is a node?
A point on the stationary wave where amplitude is always 0
What is an antinode?
A point on a stationary wave with the maximum displacement
What is the separation between 2 nodes?
Half the wavelength of the original progressive wave (λ/2)
How does phase difference change across a stationary wave?
In between adjacent nodes, all particles oscillate in phase with each other - they reach their maximum positive displacement at the same time
On different sides of a node, particles are in antiphase - particles on one side of the node reach their positive maximum displacement as particles on the opposite side reach their maximum negative displacement
Compare stationary (S) and progressive (P) waves
ENERGY TRANSFER
P - energy transferred in direction of wave
S - no net energy transfer
WAVELENGTH
P - minimum distance between 2 adjacent points oscillating in phase (eg peak and peak)
S - twice the distance between adjacent nodes/antinodes
FREQUENCY:
P - all particles oscillate at the same frequency
S - all particles other than nodes vibrate at the same frequency
AMPLITUDE
P - amplitude is constant
S - amplitude varies (max at antinode, 0 at node)
PHASE DIFFERENCE
P - (2π/λ)x, where x is distance between particles
S - nπ, where n is the number of nodes between 2 particles
How can you form a stationary wave using microwaves?
- reflect microwaves off a metal sheet so that the 2 microwaves of the same frequency travel in opposite directions
- reflected microwaves superimpose with incident waves
- this produces nodes and antinodes
How are stationary waves produced on a string?
- the string is fixed at both ends
- a progressive wave is produced along the string (either by plucking or a vibration generator)
- the progressive wave is reflected at the fixed end
- reflected wave interferes with the incident wave
- where there is destructive interference, nodes are produced
- where there is constructive interference, antinodes are produces
What is the fundamental mode of vibration?
A vibration at the fundamental frequency producing a standing wave with one antinode
What is the fundamental frequency?
- aka first harmonic, f0
* the frequency required to produce a standing wave with a single antinode in the centre and 2 nodes at either end
What is a harmonic?
A whole number multiple of the fundamental frequency
How do you work out wavelength of a stationary wave on a string?
λ = 2L/n
λ = wavelength, metres L = length of string, metres n = mode of vibration (how many antinodes there are)
How are stationary waves formed in tubes that are closed at one end and open at the other?
There must be a node at the closed end and an antinode at the open end
This means that there can only be odd harmonics
How do you work out the wavelength of a standing wave in an open-closed tube?
λ = 4L/n
λ = wavelength L= length of tube n = mode of vibration
How do stationary waves form in an open-open tube?
- both ends must have an antinode
* harmonics are possible at all integer multiples of the fundamental frequency
How do you work out the wavelength of a standing wave in an open-closed tube?
λ = 2L/n
λ = wavelength, metres L = length of tube, metres n = mode of vibration
