4.4 Waves Flashcards
what is a progressive wave?
a progressive wave carries energy from one place to another, but not matter
what are the two types of waves?
transverse and longitudinal
define longitudinal waves
waves have oscillations that are parallel to the direction of energy transfer
define transverse waves
waves which have oscillations perpendicular to the direction of the energy transfer
define displacement
Distance from the equilibrium position in a particular direction
define amplitude
the maximum displacement from the equilibrium position
define wavelength
minimum distance between two points in phase on adjacent waves, for example, the distance from one peak to the next or from on compression to the next
define period
the time it takes for one complete oscillation to occur at any point
what is anti phase
Two particles have a phase difference of 180 degrees
For example when one particle reaches its maximum displacement at the same time as the other reaches its maximum negative displacement
define phase difference
the difference in phase angle by which one wave lags behind another, measured in radians or degrees
define frequency
the number of complete oscilations that pass a point per unit time
define wave speed
the distance the wave travels per unit time
what is the equation for frequency?
f = 1/T (T = period)
what is the phase difference formula
Phase difference = x (distance between two points) / wave length x 360 (or 2pie)
Examples of transverse waves
Waves on the surface of water
all EM waves
Waves on a stretched string
S - waves produced in earthquakes
outline an experiment using an oscilloscope to determine the frequency of a wave
- used to determine the frequency of a wave
- use a microphone to generate a graph of p.d. against time (microphone converts sound waves into electrical signals)
-voltage on y axis (controlled by GAIN DIAL, volts per division), time on the x axis (controlled by TIMEBASE DIAL, seconds per division)
-each horizontal square represents a certain time interval. This is called timebase
-
use frequency = 1/t (t=period of wave in seconds) to calculate frequency
(note if the time base is turned off, the wave no longer moves across the screen making it easy to look at the intensity of the wave)
in a graphical representation of a longitudinal wave, what parts are the peaks and troughs?
rarefraction = trough (where the lines far apart) compression = peak (where the lines bunch up)
what is reflection and what is the key rule?
Reflection occurs when a wave changes direction at a boundary between two different media, remaining in the original equilibrium.
the angle of incidence is ALWAYS equal to the angle of reflection
what is refraction?
refraction occurs when a wave changes speed and direction as it travels through a different medium, this depends on how optically dense the medium is (bending of a wave)
what is diffraction?
the spreading of a wave through a small gap or around an obstacle, the effect is most significant when the gap width is equal to the wavelength, noticeable effects when the gap width is several wavelengths wide
when is diffraction effect the most significant and what happens when the wavelength is smaller than the gap size
when the size of the gap is about the same size as the wavelength of the wave
and small wave length will not diffract
when waves reflect, refract and diffract what happens in terms of speed, wave length and frequency
reflect: frequency and wavelength do not change
Refract: has affect on wavelength, but not frequency
Diffract: speed, wavelength and f do not change
what is plane polarisation? what types of waves can be polarised?
plane polarisation is when a wave is restricted so that it only oscillates in one direction, only TRANSVERSE waves can be polarised
what is the wave speed equation?
v = fλ
with questions concerning EM radiation, all EM waves travel at c = 3 x10^8
outline an experiment using a ripple tank to investigate wave effects (reflection, diffraction and refraction)
First, set up a ripple tank of water with a light directly above it and a straight bar motor connected to a paddle, the wave fronts will be visible on the screen below the tank.
REFLECTION:
-to investigate reflection place a barrier in the tank at an angle to the wave fronts, the waves will reflect off the barrier and travel in a different direction to the way they arrived, remember angle of incidence θi = angle of reflection θr
DIFFRACTION:
-to investigate diffraction place an object in the ripple tank to create a barrier with a gap in the middle of it, this gap can be varied to see the effects this has on how the waves spread through the tank, remember when the gap is close to or the same size as the wavelength = most diffraction
REFRACTION:
-to investigate refraction a glass sheet can be used to decrease the water depth and produce a region with a different wave speed
outline an experiment using polarising filters to polarise visible light
place a light source in front of two polarising filters (unpolarised light is in all directions), keep the first filter in a fixed position and rotate the second to change the intensity from maximum light to no light, rises and falls as the angle is changed remember MALUS’ LAW
what is Malus’ law and what does it tell you?
I = Io x cos^2θ
-it tells you the intensity of plane polarised light that passes through a filter
I = final intensity after passing through second filter
Io = initial max intensity
θ = angle between the first and second filter
outline an experiment to observe polarisation of microwaves
- place a metal grille in between a microwave transmitter and receiver (opposite sides of grille), connect the receiver to an ammeter
- the microwave transmitter produces vertically plane-polarised radiation
- the metal grille absorbs radiation of the same plane as the radiation meaning when the metal grille is horizontal very few of the microwaves will be absorbed so the ammeter will show a high output, when the metal grille is vertical all of the microwaves will be absorbed meaning the ammeter will show no output
what is the formula for intensity of a progressive wave and what is the relationship between intensity and amplitude?
intensity = power/area
intensity is directly proportional to amplitude squared
this comes from the fact that intensity is proportional to energy and the energy of a wave depends on the square of the amplitude
what are the main properties of EM radiation?
- they all travel at c (3x10^8m/s)
- they are transverse
- they consist of an electric and magnetic filed that are at right angles to each other and the direction of wave travel
- they can be refracted, reflected, diffracted, polarised and can undergo interfernce
what is the order of the EM spectrum?
remember hammond’s mnemonic
Radio, Micro, Infrared, Visible, Ultraviolet, X-Ray, Gamma
order of magnitude for radio
10^6 - 10^-1 m
order of magnitude for micro
10^-1 - 10^-3 m
order of magnitude for infrared
10^-3 - 7x10^-7 m
order of magnitude for visible
7x10^-7 - 4x10^-7 m
order of magnitude for ultraviolet
4x10^-7 - 10^-8 m
order of magnitude for x-rays
10^-8 - 10^-12 m
order of magnitude for gamma
10^-12m - 10^-16 m
As you go further up the electromagnetic spectrum why does it get dangerous
Because waves carry more energy as you go up the spectrum for example gamma ray is rye most dangerous
what is the formula for refractive index?
n = c/v c = speed of light in a vacuum c = speed of light in the medium
what does the refractive index tell us?
it tells us the ratio of the speed of light in the medium compared to the speed of light in a vacuum (measures how much the material slows down light)
if something has a high refractive index what does that mean about the speed of light in the medium?
slow speed
if something has a low refractive index what does that mean about the speed of light in the medium?
high speed
how does light bend when it moves into a medium with a high refractive index (slows it down)?
light bends TOWARDS the normal
how does light bend when it moves into a medium with a low refractive index (speeds it up)?
light bends AWAY from the normal
what is snell’s law?
n1sinθ1 = n2sinθ2 n1 = refractive index of first medium θ1 = angle of incidence n2 = refractive index of first medium θ2 = angle of refraction
nsinθ = CONSTANT at a boundary where θ is the angle to the normal
what is total internal reflection and when does it occur?
when the light is reflected back into the material and it occurs when the angle of refraction is above 90 degrees and therefore the angle of incidence is more than CRITICAL (when it is equal to critical is will travel along the boundary of the material at 90 degrees)
what is the critical angle equation?
sinC = 1 / n
(n = refractive index of the material)
this comes from snells law as n2 = 1 because its in air and θ2 is 90 degrees (angle of refraction) making sin90 = 1
outline an experiment to investigate total internal reflection
- shine a light ray into the curved face of a semi-circular glass block so that it always enters at right angles to the edge (this means the ray won’t refract as it enters the block, just when it leaves from the the straight edge)
- vary the angle of incidence until the light beam refracts so much that it exits the block along the straight edge, this angle of incidence is critical
- if you increase the angle of incidence so its greater than C, you’ll find the ray is reflected from the straight edge of the block (total internal reflection occurs)
what is the principle of superposition of waves?
it states that when two or more waves of the same type meet at a point, the resultant displacement at that point is equal to the sum of the displacement of the individual waves
outline an experiment to investigate two-source interference with sound waves
- connect two speakers to the same oscillator (so the waves are coherent and in phase) and place them in line with each other
- walk slowly across the room in front of them
- you will hear varying volume of sound, at the points where the sound is loudest, the path difference is a whole wavelength (nλ)
- at points where the sound will be quietest the path difference is an odd number of half wavelengths (n+0.5λ)
outline an experiment to investigate two-source interference with microwaves
(similar to sound waves & light)
- use a microwave signal generator and attach it to two transmitter cones to produce two coherent wave sources
- instead of a screen you will use a microwave receiver probe
- if you move the probe along the path of interference (straight) you’ll get an alternating pattern of strong and weak signals (just like dark and bright fringes in light experiment, or varying sound in sound experiment)
what is interference?
interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude, can be constructive or destructive
what is path difference?
refers to the difference between the distances travelled by two waves arriving at the same point, measured in λ (metres)
what is constructive interference and what is the rule for path difference when this occurs?
when the two waves superpose constructively to produce a wave with larger amplitude, can be total constructive or partially destructive
rule = nλ (whole number of half wavelengths)
what is constructive interference and what is the rule for path difference/phase difference when this occurs?
when the two waves superpose constructively to produce a wave with larger amplitude, can be total constructive or partially constructive
rule 1 = nλ (whole number of half wavelengths)
rule 2 = 0, 2π, 4π…
what is destructive interference and what is the rule for path difference/phase difference when this occurs?
when the two waves superpose destructively to produce a wave with a smaller amplitude, can be total destructive (if the two waves are in anti-phase and have the same amplitude they will cancel each other out) or partially destructive
rule 1 = n +0.5λ (odd number of half wavelengths)
rule 2 = π, 3π, 5π
why does a whole number of wavelengths result in constructive interference?
this is because a whole number of wavelengths in path difference shows that there is no phase difference (results in the waves arriving at the same point in phase)
what was Young able to do and find out from his double-slit experiment?
Young was able to find the wavelength of light and prove it wave-like properties
outline and explain Young’s Double-Slit experiment using visible light
- set up a laser source with monochromatic (red) light
- the light will pass through a single slit (with gap width comparable to wavelength) and gets diffracted to ensure the waves are coherent
- the waves reach the double slit where diffraction occurs again producing two coherent wave sources, these waves overlap and interfere
- the progressive waves will reach the screen, where they arrive in phase there will be red fringes and where the arrive out of phase there will be no light (appear dark, dark fringes)
what is the formula Young used to calculate the wavelength of light?
λ = ax/d
where a = slit spacing, x = fringe spacing, d = distance from slits to screen
what were the issues with Young’s Double Slit Experiment and what solutions are there?
-the fringes were very small and therefore the fringe spacing was very hard to measure fringe spacing
-you could increase the fringe spacing by increasing d but this would make it more faint due to decreased intensity
-to reduce percentage error in the fringe spacing you could measure several fringes and then divide by the number of fringe spacings between them
HARD TO OBTAIN ACCURATE VALUE FOR λ
what is a diffraction grating?
it is a piece of optical equipment made from glass, onto which many thousands of very thin, parallel and equally spaced grooves/slits have been made
why is a diffraction grating better to use than two slits?
- interference patterns get sharper when you diffract through more slits, improves the brightness and makes them easier to measure
- the maxima are also further apart
outline and explain the diffraction grating experiment
- set up a laser with monochromatic light (or use a filter)
- place a diffraction grating in front
- the multiple slits will diffract the light into a clear interference pattern with bright and dark fringes on the screen
explain the orders in diffraction grating experiment
the line of maximum brightness directly at the centre of the screen is the zero order, the lines on either side of the central one are the second order, then third and so on…
what would differ if you shined white light as opposed to monochromatic light through a diffraction grating?
-you would get produce a colour spectra,
the zero order would be white, the next orders (first, second and so on) would be a spectra of all the colours
-red refracts the MOST and would be furthest away, violet would be closet to the centre
what is the equation linked to diffraction grating?
dsinθ = nλ d = distance between slits (slit separation) θ = the angle the beam makes with the grating n = the order λ = wavelength
how do you work out d (the slit spacing)?
d = 1/x
where x = the number of slits per metre
how can you calculate the the maximum number of orders when doing the diffraction grating experiment?
sub θ = 90 as the diffracted rays cannot go backwards in on itself (behind)
what is a stationary/standing wave?
a stationary wave is the superposition of two progressive waves with the same wavelength, moving in opposite directions, it STORES energy unlike progressive waves
how are stationary waves formed?
you get a stationary wave when a progressive wave is reflected off a fixed boundary, which produces a wave in anti-phase to the other (with the same frequency and amplitude), the two waves travelling in opposite directions interfere and superpose producing a wave that is stationary and ‘bops’ at these resonant frequencies
what is a node?
point on the standing/stationary wave where the amplitude is zero
what is an antinode?
point on the standing/stationary wave where the amplitude is at a maximum
what do you get at a fixed boundary in terms of standing waves? (e.g closed end of tube)
a NODE
what do you get at an open boundary in terms of standing waves? (e.g open end of of tube)
an ANTINODE
outline an experiment you can perform to measure the speed of sound
- you can create a closed-end pipe by placing a hollow tube into a measuring cylinder of water
- choose a tuning fork and note down the freq. of the sound it produces (it’ll be stamped on the side of it)
- gently tap the tuning fork and hold it just above the hollow tube, the sound waves produced by the fork travel down the tube and get reflected (and form a node) at the air/water boundary
- move the tube up and down until you find the shortest distance between the top and the water level that the sound from the fork resonates at (when sound is loudest)
- this distance is a quarter of the wavelength λ/4
- multiply this by 4 and use v=fλ to work out the speed of sound in air
what is a harmonic?
a wave whose frequency is an integral (whole-number) multiple of the frequency of some reference wave, fundamental then 1st harmonic, 2nd harmonic, 3rd and so on…
what is the rule for working out the harmonic when there is a antinode at each end? (two open ends)
the harmonic no. = the number of nodes
or just count the full circles
what types of waves are produced in stringed instruments like violins and guitars?
transverse stationary waves
your finger or the bow sets the string vibrating at the point of contact, waves are sent out in both directions and are reflected back at both ends
what types of waves are produced in a wind instrument like a flute or oboe (or other air column)?
longitudinal stationary waves
- if the instrument has a closed end a node will form here, you will get the lowest resonant frequency when the length (L) of the pipe is a quarter of the wavelength
- if the instrument has an open end an antinode will form here meaning you will get the lowest resonant frequency when the length (L) of the pipe is half the wavelength
what is the distance in λ between adjacent nodes or antinodes?
λ/2, half the wavelength
what is the distance in λ between an adjacent node and antinode?
λ/4, quarter of the wavelength
what are the key differences between stationary and progressive waves?
progressive waves travel and carry energy whereas stationary waves are fixed in position and instead store energy
