Waves 2 - Stationary Waves, Interference and Diffraction Flashcards

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1
Q

How do these two progressive waves interact when they overlap?

A

Form a superposition

Displacements combined (added or subtracted) at each point

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2
Q

What happens when these two pulses overlap?

A

Constructive interference (Displacements combine)

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3
Q

What happens when these two pulses overlap?

A

Destructive interference (Displacements cancel)

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4
Q

How does a stationary wave form?

A
  1. Progressive wave reflects off a fixed point
  2. Two progressive waves propagating in opposite directions (with same c,f,λ,A)
  3. Waves overlap and interfere forming superposition
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5
Q

On a stationary wave how are nodes and antinodes different?

A

Nodes → Points of 0 amplitude

Antinodes → Points of maximum amplitude

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6
Q

How are progressive waves different from stationary waves?

A
  • All points on a progressive wave have same amplitude (Stationary waves have range)
  • Progressive waves resultant energy transfer (Stationary waves have 0 resulatant)
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7
Q

How is the wavelength of a stationary wave calculated?

A

Each loop = ½λ

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8
Q

How is the frequency of the nth harmonic of a stationary wave calculated?

A
  1. Calculate the frequency of the 1st harmonic
  2. Multiply f1 by n
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9
Q

On this stationary wave why do points A and B have different amplitudes?

A

A and B have different maximum displacements

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10
Q

On this stationary wave what is the phase difference between A,B,C and D

A

0° → All points on same side of equilibrium are in phase

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11
Q

On this stationary wave what is the phase difference between A,B,C and D

A

A and B → 180° → All points on oppsoite side of equilibrium are in anti-phase

C and D → 180°

A and C → 0° → All points on same side of equilibrium are in phase

B and D → 0°

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12
Q

How can the frequency of the first harmonic on this string be decreased?

A
  • Decrease tension (reduce mass)
  • Increase distance between end points
  • Use string with greater density (greater μ)
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13
Q

What 2 conditions are required to produce an interference pattern?

A
  1. Sources must be coherent (same frequency, constant phase difference)
  2. Sources must be monochromatic (one wavelength)
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14
Q

When will two sources interfere constructively?

A

When their path difference = nλ

So phase difference = 0°

Maxima forms

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15
Q

When will two sources interfere destructively?

A

When their path difference = (n+½)λ

So phase difference = 180° (∏ rad or antiphase)

Minima forms

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16
Q

When does maximum diffraction occur?

A

When the wavelength is close to the size of the gap the wave passes through

17
Q

What does the interference pattern of the single slit look like?

A

Large central maxima

Intensity decreases exponentially

Each maxima has half width of central

18
Q

For the single slit how is the central maxima width affected by λ?

A

W ∝ λ

19
Q

For the single slit how is the central maxima width affected by the gap size?

A

W ∝ 1/a

20
Q

For the double slit, how can you increase the widths of the maximas?

A
  1. Increase λ
  2. Increase slit to screen distance D
  3. Decrease slit separation s
21
Q

How does the intensity graph look for the double slit interference pattern?

A

Intensity decreases linearly

Width of maximas constant

22
Q

How is the 1st maxima formed for the diffraction grating

A

between adjacent slits Path difference = 1λ

So phase difference = 0°

23
Q

How is the 3rd maxima formed for the diffraction grating?

A

between adjacent slits Path difference = 3λ

So phase difference = 0°

24
Q

How do you calculate the slit separation for a diffraction grating?

A
25
Q

How do you calculate the maximum number of observed maximas for the diffraction grating?

A

nmax = d/λ

Round Down!!!

26
Q

When sound forms a stationary wave in a pipe, what 2 rules must it follow?

A

Open end(s) -> Antinode
Closed end(s) -> Node

27
Q

When sound forms a stationary wave in a pipe, why can’t you use the first harmonic equation?

A

Sound waves cannot have a tension associated with them

28
Q

When sound forms a stationary wave in a pipe closed at 1 end, what harmonics do you consider?

A

Odd harmonics
(n=1,3,5,…)