Waves 2 - Stationary Waves, Interference and Diffraction

Question 1

How do these two progressive waves interact when they overlap?

Answer 1

Form a superposition

Displacements combined (added or subtracted) at each point

Question 2

What happens when these two pulses overlap?

Answer 2

Constructive interference (Displacements combine)

Question 3

What happens when these two pulses overlap?

Answer 3

Destructive interference (Displacements cancel)

Question 4

How does a stationary wave form?

Answer 4

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

Question 5

On a stationary wave how are nodes and antinodes different?

Answer 5

Nodes → Points of 0 amplitude

Antinodes → Points of maximum amplitude

Question 6

How are progressive waves different from stationary waves?

Answer 6

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

Question 7

How is the wavelength of a stationary wave calculated?

Answer 7

Each loop = ½λ

Question 8

How is the frequency of the n^th harmonic of a stationary wave calculated?

Answer 8

1. Calculate the frequency of the 1^st harmonic
2. Multiply f₁ by n

Question 9

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

Answer 9

A and B have different maximum displacements

Question 10

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

Answer 10

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

Question 11

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

Answer 11

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°

Question 12

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

Answer 12

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

Question 13

What 2 conditions are required to produce an interference pattern?

Answer 13

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

Question 14

When will two sources interfere constructively?

Answer 14

When their path difference = nλ

So phase difference = 0°

Maxima forms

Question 15

When will two sources interfere destructively?

Answer 15

When their path difference = (n+½)λ

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

Minima forms

Question 16

When does maximum diffraction occur?

Answer 16

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

Question 17

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

Answer 17

Large central maxima

Intensity decreases exponentially

Each maxima has half width of central

Question 18

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

Answer 18

W ∝ λ

Question 19

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

Answer 19

W ∝ 1/a

Question 20

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

Answer 20

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

Question 21

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

Answer 21

Intensity decreases linearly

Width of maximas constant

Question 22

How is the 1st maxima formed for the diffraction grating

Answer 22

between adjacent slits Path difference = 1λ

So phase difference = 0°

Question 23

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

Answer 23

between adjacent slits Path difference = 3λ

So phase difference = 0°

Question 24

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

Answer 24

Question 25

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

Answer 25

n_max = d/λ

Round Down!!!