IB Physics > Waves > Flashcards

Waves Flashcards

(49 cards)

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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?

Study These Flashcards
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?

Study These Flashcards
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?

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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?

Study These Flashcards
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?

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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
How can you find the velocity at any displacement for SHM?
Use v = ± ω√(x₀² - x²) DB | Found by squaring the equation relating v and x₀, then using sin² + cos² = 1
26
How can you find the maximum displacement/velocity/acceleration of SHM?
- 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
What can be said about the energy of a system in SHM?
- 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
What does the graph for energy in a SHM system?
- Displacement (x) vs energy (y) yields a parabola and negative parabola with a TP at total energy.
29
How can you find the location of minima on a single slit interference pattern? How is it derived?
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
What does the single slit intensity graph look like? | What does a circular slit look like?
- A central peak of intensity, then much smaller peaks at either side (equally spaced). - Concentric rings of maxima and minima.
31
How does the single slit diffraction pattern change with - different slit sizes - different light colors - white light?
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
What is the condition for a bright fringe in two slit interference or a diffraction grating?
``` - 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
What does it mean for waves to be coherent?
- When waves have a constant phase difference and the same frequency.
34
What is the interference pattern of: - Two slits with negligible width? - Two slits - A diffraction grating?
- 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
How does the interference pattern appear as you increase the number of slits to N?
Primary maxima become thinner and sharper. | N - 2 secondary maxima in-between primary maxima become unimportant
36
How can you derive the equation for the location of maxima of a diffraction grating?
Consider two parallel rays emerging from neighboring slits. The path difference must equal n𝜆 for constructive interference. Use trig to derive formula.
37
How can you work out the maximum possible number of fringes for a diffraction grating?
- use dsinθ = n𝜆 DB Set θ = 90 Solve for n, round down.
38
What can cause a phase change during thin film interference?
- 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
How does thin film interference work?
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
How do you use the formulas for thin film interference? Why do they have an n?
- 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
What is the Rayleigh criterion?
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
What is resolution?
The ability to see two images/objects as distinct.
43
How do you use the Rayleigh criterion formula?
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
What is the significance of the resolution of a diffraction grating? How can you calculate it?
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
What is resonance?
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
What is the Doppler effect?
The change in the observed frequency of a wave which happens whenever there is relative motion between the source and the observer
47
How can you calculate observed frequencies of the Doppler effect?
- 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
How can you use the Doppler effect in terms of wavelength?
Use v = f'𝜆' , sub into DB eqns.
49
How can you apply the Doppler effect to light?
∆f/f = ∆𝜆/𝜆 ≈ v/c DB v = speed of observer ∆f, ∆𝜆 = observed change in frequency, wavelength f, 𝜆 = actual freq, wavelength
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