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IB Physics > Waves > Flashcards

Waves Flashcards

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1
Q

What is the defining feature of simple harmonic motion, (and the equation) and what are two examples?

A
  • a ∝ -x Acceleration is always proportional to displacement, and in the negative direction. - a = -ω²x
  • A pendulum with very small oscillations, a hanging spring that bounces up and down
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2
Q

What is the …

  • Phase difference?
  • Wavelength?
  • Amplitude?
A
  • Phase difference, ϕ, is the angle of difference between two waves (the fraction of a complete cycle). In phase = synchronised.
  • Wavelength, 𝜆, is the distance between two peaks/troughs of a wave.
  • Amplitude, A, is the max. displacement from the equilibrium position of a wave.
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3
Q

How can you calculate the displacement/position, velocity, and acceleration of a sinusoidal wave?

A

Differentiate the graph to go from s to v to a, and integrate to go back.

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4
Q

What are the features of SHM?

A
  • Follows a fixed cyclical path
  • Has a central equilibrium point.
  • Repeats at intervals (periodic)
  • Displacement, velocity, and acceleration change constantly.
  • There is a restoring force acting towards the equilibrium position.
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5
Q

What are…

  • Travelling waves
  • Wavefronts
  • Rays
A
  • Waves that can transfer energy and information without a net motion of the medium in which they travel.
  • Lines that show all the parts of the wave that are in phase.
  • A line showing the direction that the wave is travelling in, perpendicular to the wavefronts.
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6
Q

What is the difference between a transverse and longitudinal wave?

A
  • Transverse > oscillations are perpendicular to the direction of energy transfer.
  • Oscillations happen in the direction of transfer of energy - compressions and decompressions.
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7
Q

What is an experiment to find the speed of sound?

A

Set up two sound sensors a known distance apart, and make a sound in front of them. Record the difference in time that the sound wave reaches the two sensors. Change the distance and repeat the experiment, plot distance against time on a graph.

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8
Q

What equation links the different features of a wave?

A

v = f 𝜆

m/s), (Hz), (m

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9
Q

What is the superposition principle of waves?

A

The displacement of a particle along the path of more than one wave, at any time, is the vector sum of the displacements induced by each individual wave.

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10
Q

What is interference?

A

It is the result when two waves are superimposed.
When waves have displacement in the same direction, it is constructive interference.
When waves have displacement in opposite directions, it is destructive interference.

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11
Q

How are waves reflected?

A

When a wave is reflected by a fixed end, the displacement is inverted.
When there is a free end it is not inverted.

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12
Q

What is polarisation?

A

Polarised light is when waves oscillate in one plane only.

Unpolarised light oscillates in all possible orientations.

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13
Q

What is Malus’ Law?

A 
I = I₀ x cos²θ
I = The intensity of polarised light shining out of an analyser
I₀ = the intensity of light shining through the polariser
θ = The angle between the analyser and the plane of the polarisation of the light (plane of the polariser).
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14
Q

What is Snell’s Law?

A 
n₁/n₂ = sinθ₂/sinθ₁ = c₂/c₁
n₁ = the refractive index of the original medium
θ₁ = angle of incidence
c₁ = original velocity of wave
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15
Q

What conditions are needed for total internal reflection?

A
  • When light travels from a medium with high refractive index to a low refractive index. n₁ > n₂
  • When the angle of incidence is greater than the critical angle, θ₁ > θc
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16
Q

What is the critical angle, and what formula can be derived from it?

A

The angle of incidence which gives an angle of refraction of 90°.
sinθc = n₂/n₁

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17
Q

What are nodes and antinodes in two source interference?

A
  • Nodes are points along nodal lines were there is destructive interference, and thus no oscillations.
  • Antinodes are points along anti-nodal lines where there is constructive interference and thus very large oscillations.
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18
Q

What is path difference in two slit interference, and what is the requirement to have constructive/destructive interference?

A

It is the difference in distance between the paths from two slits/sources to a point on a screen.
Constructive interference occurs at points where:
PD = n𝜆 where n ∈ Z
Destructive interference occurs at points where:
PD = (n + 1/2)𝜆 where n ∈ Z
Both waves must be the same type, frequency, and wavelength.

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19
Q

How can you work out the fringe separation of two slit interference?

A 
s = 𝜆D/d
s = fringe spacing /m
D = Slit-screen distance /m
d = slit separation /m
𝜆 = wavelength /m
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20
Q

How are standing waves formed in pipes?

A
  • There is always a node at a closed end

- There is always an anti-node at an open end.

21
Q

What are standing waves, and when are they produced?

A

Its when two waves with the same frequency and wavelength are travelling in opposite directions, and interfere to create a stationary wave.

22
Q

What wavelength and frequency must be used to create standing waves?

A 
- 𝜆n = 2L/n 
L is the length of the sample of medium
n ∈ Z
𝜆n is the wavelength of the nth harmonic.
- fn = nc/2L 
fn is the frequency of the nth harmonic
nc is the harmonic no. x the wave speed.
23
Q

///////What are two SHM experiments that you have carried out?

A
  • A bobbing mass on a spring.

- A pendulum with small oscillations.

24
Q

How can you work out equations for acceleration, velocity and displacement using calculus with SHM?

A 
Say that x = x₀sin(ωt) or x₀cos(ωt) 
ω = the angular frequency, rads-1. 
x₀ = max displacement (amplitude)
- Sine or cosine depends on the displacement of the object at time t = 0.
- differentiate to find other equations.
25
Q

How can you find the velocity at any displacement for SHM?

A

Use v = ± ω√(x₀² - x²) DB

Found by squaring the equation relating v and x₀, then using sin² + cos² = 1

26
Q

How can you find the maximum displacement/velocity/acceleration of SHM?

A
  • Use the appropriate equation for x/v/a. The maximum is the coefficient of sine or cosine (max. possible value of sin or cos is 1)
27
Q

What can be said about the energy of a system in SHM?

A
  • ET = 1/2 mω²x₀² DB
  • Total energy at any time sum of KE and PE:
    ET = EK + EP
  • Equation for EP can be derived by working with these two equations and the equation for EK (DB)
28
Q

What does the graph for energy in a SHM system?

A
  • Displacement (x) vs energy (y) yields a parabola and negative parabola with a TP at total energy.
29
Q

How can you find the location of minima on a single slit interference pattern? How is it derived?

A

First minima at θ = 𝜆/b. All subsequent minima have equal spacing of 𝜆/b.
b = slit width,
θ = angle from first intensity peak to first dark fringe.
Found by considering two parallel rays separated by b/2. Show that path difference = n𝜆/2, sinθ ≈ θ

30
Q

What does the single slit intensity graph look like?

What does a circular slit look like?

A
  • A central peak of intensity, then much smaller peaks at either side (equally spaced).
  • Concentric rings of maxima and minima.
31
Q

How does the single slit diffraction pattern change with

  • different slit sizes
  • different light colors
  • white light?
A

Use the formula θ = 𝜆/b:

  • bigger slit, closer fringes
  • longer wavelength, further fringes.
  • diff patterns for different colors superimposed: white central maximum, colored fringes (blue light gets diffracted the least)
32
Q

What is the condition for a bright fringe in two slit interference or a diffraction grating?

A 
- dsinθ = n𝜆 DB
d = slit separation
n = an integer (0 for first maximum)
D = distance to screen
The separation (s) can be found through trig and the approximation that tanθ ≈ θ
33
Q

What does it mean for waves to be coherent?

A
  • When waves have a constant phase difference and the same frequency.
34
Q

What is the interference pattern of:

  • Two slits with negligible width?
  • Two slits
  • A diffraction grating?
A
  • Intensity (y) versus angle (x) yeids a sinusoidal wave of constant intensity, evenly spaced maxima.
  • The double slit pattern is modulated by the single slit pattern: double slit “cut off’” under single slit pattern.
  • Thin evenly spaced maxima of roughly the same intensity.
35
Q

How does the interference pattern appear as you increase the number of slits to N?

A

Primary maxima become thinner and sharper.

N - 2 secondary maxima in-between primary maxima become unimportant

36
Q

How can you derive the equation for the location of maxima of a diffraction grating?

A

Consider two parallel rays emerging from neighboring slits. The path difference must equal n𝜆 for constructive interference. Use trig to derive formula.

37
Q

How can you work out the maximum possible number of fringes for a diffraction grating?

A
  • use dsinθ = n𝜆 DB
    Set θ = 90
    Solve for n, round down.
38
Q

What can cause a phase change during thin film interference?

A
  • Reflection at an optically denser medium causes a phase change of π
  • No phase change when a wave traveling in a more optically dense medium is reflected at the boundary of a less optically dense medium.
39
Q

How does thin film interference work?

A

Light incident on a film of oil width d is partially reflected (phase change of π). Some light is also reflected off the surface of the water. The two reflections interfere constructively and destructively for different wavelengths of light.
2dn = (m + 1/2)𝜆 (constructive)
n = refractive index of oil.
𝜆 = wavelength in original medium

40
Q

How do you use the formulas for thin film interference? Why do they have an n?

A
  • Draw a diagram, note if there are any phase changes. Formulas designed for 1 phase change.
  • To account for shorter wavelength in oil. 𝜆oil = 𝜆/n
41
Q

What is the Rayleigh criterion?

A

Two sources are just resolved if the central maximum of the diffraction pattern of one source falls on the first minimum of the other. (imagine an intensity graph)

42
Q

What is resolution?

A

The ability to see two images/objects as distinct.

43
Q

How do you use the Rayleigh criterion formula?

A

θD = 1.22 𝜆/b DB
θD = Angular separation of two sources
b = aperture width (m)
θD can be approximated by θD ≈ s/d (separation/distance)

44
Q

What is the significance of the resolution of a diffraction grating? How can you calculate it?

A

It shows you the smallest angle at which two lines (different wavelengths) can be resolved.
R = 𝜆avg / ∆𝜆 = mN
∆𝜆 = difference in wavelength between two lines.
m = order of fringe
N = total no. of slits on grating

45
Q

What is resonance?

A

If the frequency of the force driving the oscillations of a system matches the natural frequency of a system, large amplitude oscillations will occur, known as resonance.

46
Q

What is the Doppler effect?

A

The change in the observed frequency of a wave which happens whenever there is relative motion between the source and the observer

47
Q

How can you calculate observed frequencies of the Doppler effect?

A
  • f’ = f( v / v ± us) DB
  • f’ = f( v ± uo / v) DB
    f’ = observed frequency
    us, uo = velocity of source, observer
    v = wave speed [note that for a moving observer, the medium will change to moving air]
    f = frequency of source.
    Choose ± depending on moving away or moving closer. Decide if the observer will meet the wavefronts more or less frequently.
48
Q

How can you use the Doppler effect in terms of wavelength?

A

Use v = f’𝜆’ , sub into DB eqns.

49
Q

How can you apply the Doppler effect to light?

A

∆f/f = ∆𝜆/𝜆 ≈ v/c DB
v = speed of observer
∆f, ∆𝜆 = observed change in frequency, wavelength
f, 𝜆 = actual freq, wavelength

IB Physics (12 decks)

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