Module 2 Waves Flashcards
what is a transverse wave?
ocillations or vibrations which are perpendicular to the direction of energy transfer
what does a progressive way do? and what are some ways you can tell waves carry energy?
- a progressive wave carries energy from one place to another without transferring any material
- the transfer of energy is the same direction as the waves is travelling
e. g
1. ) electromagnetic waves cause things to heat up
2. ) X-rays and gamma rays knock electrons out of their orbit, causing ionisation
3. ) loud sounds cause large oscillations in air particles which can make things vibrate
4. ) wave power can be used to generate electricity
what are some examples of transverse waves?
- waves on the surface of warer
- any electromagnetic wave
- waves on stretched strings
- S-waves produced in earthquakes
what is a longitudinal wave?
in longitudinal waves the oscillations are parallel to the direction of the energy transfer
what are examples of longitudinal waves?
- sound waves
- p waves produced in earthquakes
suggesr why speed of sound is faster through a medium with higher density?
particles are closer together
strong restoring force/ vibrations are passed more rapidly from one particle to the next
what is the displacement of a wave?
give the symbol and unit
-how far a point on the wave has moved from it undisturbed position
symbol= x
unit= metres
what is the amplitude of a wave?
give the symbol and unit
the maximum magnitude of the displacement
symbol= A
unit= metres
what is the wavelength of a wave?
give the symbol and unit
the length of one whole wave cycle e.g from crest to crest ot trough to trough
symbol= λ
unit= metres
what is the period of a wave?
give the symbol and unit
the time taken for a whole cycle (vibration) to complete
symbol= T
unit= seconds
what is the frequency of a wave?
give the symbol and unit
the number of cycles (vibrations) per second passing a given point
symbol= f
units= hertz
what is the phase of a wave?
a measurement of the position of a certain point along the wave
unit= degree or radians
what is the phase difference of a wave?
-state unit
the amount one wave lags behind another
unit= degree or radians
what is a CRO oscilloscope? what does it do?
- a cathode ray osscilloscope measures voltage
- it displays waves from a signal generator as a function of voltage over time
- the displayed wave is called a trace
- the screen is split into into sqaures called divisions
- the vertical axis is in volts. the volts per division is controlled by the gain dial
- the horizontal axis is in seconds- also called the timebase. the seconds per divisions shown on this axis is controlled by the time base dial
- you can alter the gain and timebase to make it easy to read off measurements
the frequency is inverse of the period
show this in a equation
what are the units
f= 1/T
frequency= 1/Period
Hz= 1s-1
what are the eqautions for wave speed? what are you measuring in this eqaution?
wave speed= distance/ time
v= d/t
speed of wave= frequency x wavelength
v= fλ
you are measuring how fast a point on the wave pattern moves
if particles are oscilatting in step with each other (they both reach their maximum positive displacement at the same time) what are they described as?
in phase
they have a phase difference of 0
what is meant by a wave profile graph?
a graph showing the displacement of the particles in the wace against the distance along the wave
(the graph shows a snapshot of the wave)
what can a wave profile be used to determine?
- the wavelength of the wave
- amplitude of the wave
- the displacement (as the displacement of the particles in the wave is continously changing, the wave profile changes shape over time)
- )if two particles are seperated by distance of one whole wavelength what is the size of their phase difference?
- )what is they were two complete cycles out of step
- )360 degrees or 2π radians
- ) 720 degrees or 4π
if particles are oscillating completely out of step with each other then what are they described as being?
what is their phase difference?
the particles are described as being in antiphase
their phase difference is 180 degrees or π radians
when does reflection occur?
when a wave changes direction at a boundary between two different media, remaining in the original medium
what does a ray show?
the direction of energy transfer and so the path taken by the wave
what does the law of reflection state?
the law states that the angle of incidence is equal to the angle of reflection
when does refraction occur?
(what is meant by partial reflection?)
refraction occurs when a wave changes direction as it changes speed when it passes from one medium to another
when the wave refracts there is always some reflection of the surface (partial reflection)
what happens (in terms of refraction near the normal) when a wave speeds up?
when a wave speeds up it refracts away from the normal
what happens (in terms of refraction near the normal) when a wave slows down?
when waves slow down they refract towards the normal q
what effect does refraction have on a wave?
- it effects the wavelength of the wave (but not its frequency)
- if the wave slows down it wavelength decreases and the frequency remains unchanged
- if the wave speeds up its’s wavelenght increases and the frequency remains unchanged
what is meant by diffraction?
this when a wave passes through a gap or travel around an obstacle and they spread out
what affects how much a wave diffracts?
- the size of wavelength
- size of gap
- size of obstacle
when are diffraction effects most significant?
whent the size of the gap or obstacle is about the same size as the wavelength of the wave
why is can you hear a conversation coming from aroung a corner but can not see the light coming from the room?
- sound diffracts when it passes through a doorway allowing you to hear the conversations
- this is because the wavelength of sound is similar to the size of the gap
- however light has a much smaller wavelength, so it does not diffract through such a large gap
what is meant by polarisation?
polarisation is where the wave particles oscillate along in one direction only (up and down in the vertical direction)
which means that the wave is confined to a single plane.
what is meant by the plane of oscillation?
the plane of oscillation contains the oscillation of the particles and the dirtection of the travel of the wave
why cant longitudinal waves not be plane polarised?
- their oscillations are always pararrel to the direction of energy transfer
- their oscillatiobns are alreadt limited to only one plane (the direction of energy transfer)
what is meant by plane polarisation?
this is where you polarise a wave so that it only oscillates in one direction
what is meant by partial polarisation?
this is where tranverse waves reflect off a surface and more of them are oscillating in one particular plane, but the wave is not completely plane polarised
what does a polarising filter do?
it only transmits vibrations in one direction
what happens if you have two polarising filters at right angles to each other?
no light will get through
how can you investigate the polarisation of light using two polarising filters?
- ) align the transmission axes of two polarising filters so they are both vertical. shine unpolarised light on the first filter. keep the position of the first filter fixed and rotate the second one
- ) light that passes through the first filter will always be vertically polarised
- ) when the transmission axes of the two filters are aligned, all of the light that passes through the first filter also passes through the second.
- ) As you rotate the second filter, the amount of light that passes through the second filter varies
(just like vectors, you can think of the transmission axis of the rotating filter as having a vertical and horizontal component. The larger the vertical component, the more vertically polarised light will pass through the filter)
5.) As the second filter is rotated less light will get through it as the vertical component of the second filter’s transmission axes decreases. This means that the intensity of the light gettin through the second filter will gradually decrease
what is meant by intensity of a progressive wave?
what are the units for intensity?
the radiant power passint through a surface per unit area
-W m-2
what is the eqaution for intensity?
I = P/A
intensity= (radiant) Power/ cross-sectional area
what happens to the intensity when the distance doubles?
if the distance doubles the intensity decreases by a factor of 4 (22)
what happens to the intensity of the distance increase by a factor of 100?
if the distance increase by a factor of 100 then the intensity will be 1002
why do ripples decrease in height and travel at less speed from a source of energy?
- when ripples travel out across the surface of a pond the intensirty drops as the energy becomes more spread out
- this causes a drop in amplitude (the ripple height decreases the further the wave is from the source)
- decreased amplitude means a reduced average speed of the oscillating particles
- halving the amplitude results in particles oscillating with half the speed, and a quarter of the kinectic energy (Ek= 1/2mv^2)
what is the relationship between intensity and amplitude of a wave?
for any wave the intensity is directly proportional to the square of the amplitude.
Double the amplitude of a wave and the intensity will quadruple
what is the relationship between distance and amplitude?
Intenisty is inversely proportional to the distance from the source ( I ∝ 1/d)
if the distance doubles the intensity decreases by a factor of 4 (gets squared)
if the distance increases by a factor of 100 the intensity will be 1002 smaller
what are the properties of electromagnetic waves?
- all EM waves travel in a vacuum at a speed of 3.00 x 108 ms-1
- they are transverse waves consisting of vibrating electric and magnetic fields
- all EM waves can be refracted, reflected and diffracted and can undergo interference. They also obey velocity= frequency x wavelength
- progressive EM waves caryy energy
- EM waves are transverse so they can be polarised
what is the eqaution for the speed of electromagnetic waves through a vacuum/ air?
c= f λ
c= 3.00 x 108 ms-1
f= frequency
w= wavelength
what do you call a polarising filter? what does it do?
- polarisers
- this polarises unpolarised electromagnetic waves by only allowing em waves that are polarised in the same direction as the filter to pass through
what are polaroid filters?
plastic films that contain very long thin crystals and polarise light.
how are unpolarised microwaves polarised?
a metal grille is used
why does the intensity drop to zero when the direction of vibration in the microwaves is aligned with the wired in the metal grille?
- because the grille is absorbing their energy
- the vibrating electric field of the microwave excites the electron in the metal grille
- the energy of the incoming microwaves is absorbed and re-emitted in all directions
- only a few of those re-emmited waves are vibrating in the direction of the microwave reciever, however these waves may not be picked up because the receiver only receives microwaves in one plane.
exam questions:
two polarising filters are placed on top of each other and held in front of a source of white unpolarised light
a. ) no light can be seen through the filters. state the angle between the transmission axes of the two filters
b. ) the filters are rotated so that the angle between their transmission axes is 45 degrees. describe the difference in the intensity of light once it has passed through both filters compared to the light once it has only passed through the first filter.
a. ) they are at right angles to one another (90 degrees)
b) It would be half the intensity of the orginal light (because at 25 degrees the vertical and horizontal contributions are eqaul so the intensity is halved between them.)
what is refraction?
this is the way a wave chnages direction as it enters a different medium.
the change in direction is a result of the wave slowing down or speeding up
if the ray bends towards the normal what does this mean?
the ray is slowing down
the ray is going from a less optically dense material to a more optically dense material
if the ray bends way from the normal what does this mean?
the wave is speeding up
it goes from an optically denser material to a less optically dense material
what is the refractive index and what does it measure?
the absolute refractive index of a material, n, is the ratio between the speed of light in a vacuum, c, and the speed of light in that material, v.
n= c/v
it measures how much a material slows down light
the greater the refractive index the ______ the light entering the material is reflected towards the normal.
the greater the refractive index the more the light entering the material is reflected towards the normal.
express snell’s law in an eqaution that is used to calculate the refractive index
n= refractive index of the material light travels in
θ= the angle the light ray makes with the normal of the boundary
what can you use to calculate the refractive index?
a refractometer
what are two conditions required to total internal reflection?
- ) light must be travelling from a higher to a lower refractive index
e. g TIR is impossible when light in glass meets air but not the other way round - ) the angle at which the light strikes the boundary must be above the critical angle.
what is the critical angle?
the angle of incidence at the boundary between two media that will produce an angle of refraction of 90 degrees
what is the eqatuion for finding the criticle angle?
sin C= 1/n
C= critical angle
n= refractive index of the material
what does superposition refer to?
when two waves of the same type meet and pass through each other producing a single wave with the displacements of each wave combined
what does the principle of superposition state?
the principle of superposition states that when two waves meet at a point the resultant displacement is equal to the sum of the individual displacements of the individual waves.
what is meant by interference?
this is where two or more waves superpose with each other
what happens in constructive interference?
- when two waves are inphase
- the maximum positive displacements from each wave line up
- creating a resultant displacement with increased amplitude
what do constructive waves do to intensity?
they increase intensity
-because the size of amplitude is proportional to intensity, so as intensity increases as the amplitude also increases
what is meant by destructive interference?
- this is when two waves are in anti-phase
- so the maximum positive displacement from one wave lines up with the maximum negative displacement from the other
- the resultant displacement is smaller than for each individual wave.
(crest plus trough of equal size, if it isnt then the destructive interfence is not total and is not noticeable)
if the waves are inphase and have the same amplitude what will happen to the resultant amplitude?
the resultant amplitude will be 0
the new wave is cancelled out completely
state and explain the type of interfernce used by noise-cancelling headphones
- destructive interference
- in order to cancel out the sound waves from the surrounding environment
to get clear interference patterns what do the two sources (emitting waves) have to be?
coherent
what makes two sources coherent?
- if they have the same;
- wavelength
- frequency
- fixed phase difference between them
what is meant by the maximum (waves)?
the point of greatest amplitude in an interference pattern, produced by constructive interference
what is meant by minimum (waves)
the point of least amplitude in an interference pattern, produced by destructive interfernce
what is meant by path difference?
-the difference in the distance travelled by two waves from the source to a specific point
when two sources are emitting coherent waves when do you get constructive interference?
- when the path difference is a whole number of wavelenghts e.g. 0, λ, 2λ, or just nλ
- at any point an eqaul distance from both sources
when two sources are emitting coherent waves when do you get destructive interference?
-at any point where the path difference is an odd number of half wavelengths
explain why you might have difficulty in observing interfernce patterns in an area affected by two waves from two sources even though the two sources are coherent?
interference will only be noticeable if the amplitudes of the two waves are approximately eqaul
refer back to this diagram
what can you use to produce coherent waves?
an osicillator e.g
one ociscillator being connected to two loudspeakers to create two sound waves
discuss Young’s double Slit experiment
- ) Young used a monochromatic source of light (one wavelength present) (which was achieved by using a colour filter than only allowed a specific frequency of light to pass) and a narrow slit near the same size of the wave to diffract the light
- ) The diffracted light arrives at the double slit in phase
- ) It is then diffracted again from the double slit, each slit acting like two coherent point sources
- ) the coherent waves spread and overlap forming interference pattern that as seen on the sceern as alternating bright and dark fringes
- where it was dark destructive interference was taking place (1/2λ, 1 1/2λ)
- where it was light constructive interference was taking place (0, λ, 2λ)
how can you find the wavelength of the wave producing an interference pattern from two coherent sources
λ= ax/ D
λ= wavelength
a= distance between the two sources of coherent waves
x= seperation between two maximums or two minimums (distance between to light fringes/ dark fringes)
D= distance from the source of coherent waves to the screen/receiver showing the light and dark fringes
-this equation only applies if a is smaller than D
how can you apply Young’s double slit experiment to finding two- source interference of microwaves
- ) replace the laser and slits with two microwave transmitter cones attached to the same signal generator
- ) replace the screen with a microwave reciever probe
3,) if the you move the probe along the path of the interfering coherent waves you will get an alternating pattern of strong and weak signals
what is the benefit of increasing the diffraction gradient in Young’s double-slit experiment (increasing the number of slits)
- you get the same shaped pattern as for two sits but the bright bands are brighter and narrower and dark areas between are darker
- this because when monochromatic light is passed through a grating withs 100s per mm the interference pattern is really sharp since there are so many beams reinforcing the pattern
- sharper fringes make for more precise measurements as they are easier to tell apart and so easier to measure
what do you call the line of maximum brightness (Young’s double slit experiment)?
the zero order
-the lines just either side of the central line are called first order line and the next pair out are called second order lines
state the eqaution used for calculating the wavelength of light using a diffraction gradient
d sin θ = nλ
where:
d= the slit seperation e.g you might have 99 slits instead of 2
n= what order maximum you’re observing e.g 2nd , 3rd order etc.
θ = the angle between the maximum and the incident light (zero order/ central line)
what general conclusions can you get from the diffraction gratings eqaution?
what happens when you shine white slight through a diffraction grating?
- a spectra is produced
- at the zero order maximum it is still white because all the wavelengths just pass straight through
- and then other order maximums each become a spectrum with red on the outside and violet on the inside
what is meant by a stationary/standing wave?
a wave that remains in a constant position with no net transfer of energy and is characterised by its nodes and antinodes
how can you produce a standing wave froma string?
you use melde’s apparatus
- you use a signal generator to produce a signal where you can alter the frequency and the amplitude
- output of this signal generator is then connected to a vibration generator which allows you to have something that oscillates at a particular frequency
- the vibration is then attached to a string that is attached to a pully (weights on the end) to keep it in tension
- you can seen progressive waves along the string and at a certain point they are reflected back again
- as you increase the frequency you will see places that dont move at all whch are the nodes and place where there is the maximu displacement which is the antinode
- a distance from a node to a node is half a wavelength
compare the propertices of stationary and progressive waves in terms of energy transfer, wavelength, phase difference and amplitude?
Energy Transfer
PW - net energy is transferred in the direction of the wave
SW- net energy is not transferred in stationary waves but is stored
Wavelength
PW -a whole wave length is equal to the minimum distance between two adjacent points oscillating in phase e.g between two peaks
SW -a whole wavelength is eqaul to twice the distance between two adjacent nodes (or antinodes)
Phase Difference
PW -the phase chanhes across one complete cycle of the wave
SW- all parts of the wave where there is a node is inphase and all other parts where it is antinode is antiphase
Amplitude
PW- all parts of the wave have the same amplitude (assuming no energy is lost to the surroundings)
SW- maximu amplitude occurs at the antinode then drops to 0 at the node
when is a node formed in a stationary wave?
because the two waves have the same frequency there are certain points where the waves are in antiphase
- at this point the displacement cancels out so displacement= 0
- amplitude and intensity are zero
when is a antinode formed in stationary waves?
-at points of maximum amplitude (and therefore intensity)
is energy emitted by stationary waves?
no
what is the distance between two adjacent nodes or antinodes?
1/2 a wavelength (1/2 λ)
what is the distance between a node and an antinode?
1/4 of wavelength
what is meant by resonant frequency?
frequencies at which the reponse amplitude is a relative maximum
(resonance is the tendency of a system to oscillate with greater amplitude at some frequency than at others)
what is the fundament frequency then state what is meant by the fundamental mode of vibration
fundamental frequency= the lowest frequency at which an object can vibrate
fundamental mode of vibration= a vibration at the fundamental frequency
when you have a string in fixed postion that is oscillating at the ends of the string it can not move.
what do you call these parts of the wave/ oscillating spring
the nodes because its an area of no movement and 0 displacement
what is a harmonic?
a whole-number multiple of the fundamental frequency (e.g 1st harmonic is the fundamental f, then you have the 2nd harmonic which is 2 x f, 3rd which 3 x f and so on)
if the fundamental frequency of a stationary wave (in a string) is 20Hz (f0) with a λ= 2L then what will be the frequency of the stationary wave at the 2nd, 3rd, 4th, 5th harmonic
state what the wavelength would be eqaul to for each harmonic
L= length of string
how can a stationary wave form in a tube that is closed at one end?
-if there is an antinode at the open end (where the oscillation of the air are at their greatest amplitude) and a node at the closed end (where air cannot move)
discuss standing waves in a tube in with an open end
- from fixed closed end of the tube to the open end is a node to an antinode which is a distance of a λ/4 (this is your fundamental)
- so then if you increase the frequency reducing wavelength so there is more nodes and antinodes in the tube then you calculate the total distance
e. g if you had a node, antinode, node then antinode then the distance from the first node to last antinode is 3/4 of λ. (3rd harmonic)
In tubes with one closed end you dont get even numbers of harmonics, each one is odd
what are the two ends called of a stationary wave in a tube with two open ends
-antinode
