Topic 9: Wave phenomena (HL) Flashcards
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ω2x0cos(ωt)
acceleration
(a)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ω2x0
MAXIMUM acceleration
(amax)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ωx0 sin(ωt);
(??) = ωx0 cos(ωt)
velocity
(v)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ωx0
MAXIMUM velocity
(Vmax)
[DATA BOOKLET] Equation for [???] in SHM = x0 sin(ωt); = x0 cos(ωt)
displacement (x)
How do you know whether to use -sin(ωt) or cos(ωt) for velocity in SHM?
for SHM the derivation depends on the original displacement graph/function. [if displacement was sin(ωt) then velocity will be cos(ωt); if displacement was cos(ωt) then velocity will be -sin(ωt)]
How does the total energy of a system change during SHM?
it stays constant (total energy = kinetic energy + potential energy)
What is the shape of a displacement graph for simple harmonic motion (SHM)?
Sinusoidal
Write SHM as an equation
a = -(ω2)x
What is acceleration proportional to in SHM?
negative displacement (a ∝ -x)
What is the restoring force in a simple pendulum?
m⋅g⋅sinθ
What is x0?
maximum displacement (amplitude)
When in kinetic energy maximum in SHM?
displacement = 0; x = 0
When in kinetic energy minimum in SHM?
at maximum displacement (amplitude)
x = x0
When in potential energy maximum in SHM?
displacement = x0; at maximum displacement (amplitude)
When in potential energy minimum in SHM?
displacement = 0
x = 0
In what direction does the acceleration in SHM act?
Towards the equilibrium point
(x=0)
What is ω and its unit?
angular frequency
rad s-1
How do you identify if SHM is taking place?
- Identify forces when object is displaced from rest position (free-body diagram)
- Calculate resultant force using Newton’s second law: if the force is proportional to displacement and the direction is always towards rest position, then there is SHM.
- ω2 = (restoring force per unit displacement/mass)
Assumptions for SHM (vertical spring)
- mass of spring is negligible (compared to the mass of load)
- friction (air friction) is negligible
- spring obeys Hooke’s law at all times (elastic limit is not exceeded)
- gravitational field strength, g, is constant
- the spring’s fixed end cannot move
Assumptions for SHM (simple pendulum)
- mass of the pendulum is negligible compared to that of the load
- friction (air friction) is negligible
- the maximum angle of swing is small (≤ 5
[DATA BOOKLET]
What does each symbol mean and what is its unit?
ω = 2π/T
ω is angular frequency, in rad s-1
T is time period, in s
Equation for velocity in SHM (no trig functions)
v = ±ω√( x02 - x2 )
If displacement follows a positive sin function, what functions will velocity and acceleration follow?
x = sin ωt
v = cos ωt
a = -sinωt
[NOTE: these are not the full equations, just the trig function part]
If displacement follows a negative sin function, what functions will velocity and acceleration follow?
x = -sin ωt
v = -cos ωt
a = sin ωt
[NOTE: these are not the full equations, just the trig function part]
If displacement follows a positive cos function, what functions will velocity and acceleration follow?
x = cos ωt
v = -sin ωt
a = -cos ωt
[NOTE: these are not the full equations, just the trig function part]
If displacement follows a negative cos function, what functions will velocity and acceleration follow?
x = -cos ωt
v = sin ωt
a = cos ωt
[NOTE: these are not the full equations, just the trig function part]
What was Huygen’s principal?
treat a wavefront as a number of wave sources
When does maximum diffraction occur?
when the gap is the same width as the wavelength of the wave passing through it
What is the single slit equation?
θ = (nλ)/b
- θ is the angle between the middle of the slit to the fringe (minimum)
- n is the fringe (minimum) number
- λ is the wavelength
- b is the slit width
What is diffraction?
the bending of waves around a barrier or through an opening.
How does increasing wavelength affect the angle of diffraction?
Increasing wavelength increases the angle of diffraction
θ = (nλ)/b
How does increasing slit width affect the angle of diffraction?
Increasing slit width decreases the angle of diffraction
θ = (nλ)/b
What assumptions does single slit diffraction make about the LIGHT SOURCE?
- Coherent
- Monochromatic (one wavelength)
What assumptions does single slit diffraction make about the experiment setup?
- D, distance between slit and screen is much greater than the slit width, b.
- Therefore, sinθ is roughly equal to θ
On a graph, what is the width on the central maximum equal to?
2θ
How does increasing the wavelength affect the graph/diffraction pattern?
The maxima become more spaced out
Why is it common to observe sound waves diffracting but not light waves?
Sound waves have a much larger wavelength and therefore diffract more (maximum diffraction occurs when openings are equal to wavelength) therefore can diffract through doors whereas light cannot.
Explain constructive interference using keywords
- Two waves interact
- In phase: phase difference is 0 or a multiple of 2π rads
- Maxima of each wave superimpose - larger maximum
- Amplitude = sum of the amplitude of both waves
Explain destructive interference using keywords
- Two waves interact
- Out of phase: path difference is an odd number of π rads
- The amplitudes negate each other
- Amplitude is the sum of the amplitude of both waves (one of them being negative)
If two coherent waves interact but have a path difference of half a wavelength, what happens?
Destructive interference
Describe what a diffraction pattern looks like
A line of light with lighter and darker fringes, the brightest being at the centre. They progressively get darker the further away from the centre it is.
Phase and path difference for constructive interference
Phase difference is either zero or a multiple of 2π rads
Path difference is nλ
Phase and path difference for destructive interference
Phase difference is an odd multiple of π rads
Path difference is (n + [1/2]) λ
What happens are you increase the number of slits?
- Bright fringes stay in the same position
- They become sharper and more defined
- Overall intensity is conserved (Intensity is proportional to the square number of slits)
How do you work out the number of slits per metre?
(1 / d)
where d is the distance between slits
How do you work out the distance between slits from the number of lines per metre?
( 1 / N )
where N is the number of lines per metre
What is the diffraction grating equation?
d•sinθ = n•λ
where d is the distance between slits
θ is the angle from the normal
n is the order number (starting at 0)
λ is the wavelength
How can you find the maximum number of orders?
1) set θ to 90° as this is the maximum angle it could be
2) put into the equation and work out for n
3) whatever your answer always ROUND DOWN to the nearest integer
What is the phase change when light is reflected back from an optically LESS dense medium?
No phase change for reflected way and transmitted wave
What is the phase change when light is reflected back from an optically MORE dense medium?
Reflected wave: π rads or 180° phase change
Transmitted wave: no phase change
What is the path difference of a wave reflected back from a MORE dense medium?
Phase difference is π rads, therefore, is equivalent to a path difference of (1/2) λ
What the path difference for the wave that goes through and is internally reflected by the film?
(Roughly) 2 x film thickness x refractive index
What is the total path difference for thin parallel films? (for small angles)
Roughly 2dn+(λ/2)
where d is the film thickness
n is the refractive index
λ is wavelength
What is the total path difference for thin parallel films? (Accurate, for larger angles)
(2d•n•cosθ)+(λ/2)
where d is the film thickness
n is the refractive index
θ is the angle between the refracted wave and the normal
λ is wavelength
What applications does thin parallel film diffraction have?
Anything that seeks to be non-reflective such as solar panels
Measuring the impact/ thickness oil spills
What is resolution?
The ability of an imaging system to produce two separate, distinguishable images of two separate objects
What does the Rayleigh Criterion state?
Two sources are just resolved if the principal maximum from one diffraction pattern is is no closer than the first minimum of the other diffraction pattern
General equation for the minimum angle of resolution for all apertures
θmin = λ/b
where θmin is the minimal angle for resolution
λ is the wavelength
b is the aperture size
Equation for angular separation
θs = (s/r)
where θs is the angular separation
s is the separation distance
r is the distance from observer to source
Equation for the minimum angle of resolution for circular apertures
θmin = 1.22(λ/b)
where θmin is the minimal angle for resolution
λ is the wavelength
b is the aperture diameter
What happens to the resolution if aperture size increases?
resolution increases
What happens to the resolution if wavelength increases?
resolution decreases
What happens to the resolution if aperture size decreases?
resolution decreases
What happens to the resolution if wavelength decreases?
resolution increases
How big does the angular separation need to be to resolve (see clearly according to the Rayleigh criterion)
θs ≥ θmin
the angular separation must be greater than or equal to minimum resolution angle to resolve (if equal, then it is just resolved)
What is the resolvance for a diffraction grating?
(wavelength)
the ratio of the average wavelength of light to the smallest difference in wavelengths that can be resolved by the grating
given as R = (λ/Δλ)
where λ is the average wavelength
Δλ is the smallest difference in wavelength
How do you work out the lines per millimetre?
lines illuminated/line width (in mm)
What is the resolvance for a diffraction grating?
(illuminated slits)
the total number of slits illuminated by the incident beam multiplied by the order of the fraction
given as R = mN
where m is an interger
N is the number of slits
What is the doppler effect?
the apparent frequency of waves (sound) change due to the relative movement of the source and/or the observer i.e. the frequency emitted is the same, but the observer experiences a different frequency
If you are stationary and the source is travelling towards you, what frequency will you experience compared to the frequency emitted?
the frequency experienced will be greater than the frequency emitted
If you are stationary and the source is travelling away from you, what frequency will you experience compared to the frequency emitted?
the frequency experienced will be smaller than the frequency emitted
If you are stationary and the source is travelling towards you, what wavelength will you experience compared to the wavelength emitted?
the wavelength experienced will be smaller than the wavelength emitted
If you are stationary and the source is travelling away from you, what wavelength will you experience compared to the wavelength emitted?
the wavelength experienced will be greater than the wavelength emitted
Equation for wavelength (using speed and frequency)
λ = v/f
wavelength = wave speed/frequency
[DATA BOOKLET}
Moving source, stationary observer.
What sign would you use if the source is moving towards the observer?
use –
[DATA BOOKLET}
Moving source, stationary observer.
What sign would you use if the source is moving away from the observer?
use +
[DATA BOOKLET}
Moving observer, stationary source.
What sign would you use if the observer is moving towards the source?
use +
[DATA BOOKLET}
Moving observer, stationary source.
What sign would you use if the observer is moving away from the source?
use –
When does a sonic boom occur?
When the speed of the source is equal/greater than the speed of sound
What steps should you take for echolocation (such as bats)?
1) Make the prey the observer, what frequency does it receive first?
2) This frequency is then reflected back to the predator, which is now the observer
i. e. you will have to use the Doppler formulae twice
