4.4 Waves Flashcards
what is a progressive wave?
a progressive wave carries energy from one place to another without transferring any material, the transfer of the material is in the same direction as the wave
what are the two types of waves?
transverse and longitudinal
define longitudinal waves
waves which have oscillations parallel to the direction of the wave (or wave propagation)
define transverse waves
waves which have oscillations perpendicular to the direction of the wave (or wave propagation)
define displacement
the distance a point on a wave has moved from its undisturbed/equilibrium/rest position, can be positive OR negative, measured in metres
define amplitude
the maximum displacement, the distance from a peak or trough to its rest position, measured in metres
define wavelength
the distance between two successive identical points on a wave that have the same pattern of oscillation
define period
the time it takes for one complete oscillation to occur at any point
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)
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 bounces off a surface and changes direction when it hits a boundary, 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
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 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
how does polarisation work?
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.
as the second filter is rotated horizontally, less light will get through it as the vertical component of the second filter’s transmission axis decreases which means the intensity through the second filter decreases
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
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
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
what is the principle of superposition of waves?
it states that when two or more waves of the same type meet, the resultant wave can be found by the vector addition of the displacements of the individual waves
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
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…
at resonant frequencies how many wavelengths fit onto the string?
an exact/whole number of HALF wavelengths fits onto the string
what is the rule for working out the harmonic when there is a node at each end? (two fixed ends)
the harmonic no. = no. of antinodes
or just count the full circles
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 is the rule for working out the harmonic when there is a node at one end and an antinode at the other? (one fixed end and one open end)
the harmonic no. = (no. of nodes + antinodes) - 1
or just count the full circles and multiply by 2
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
