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
4. This forms areas of maximum and minimum amplitude (nodes)

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?

How many wavelengths from each other are

• 2 nodes
• 2 anti-nodes
• A node and anti-node

Answer 7

Each loop = ½λ

Node → Node = ½ wavelength

Anti-node → Anti-node = ½ wavelength

Anti-node → Node = ¼ or ¾ wavelength

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 and the same 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!!!

Question 26

What are the requirements for superposition?

Answer 26

The waves must be of the same type, passing through the same medium at the same time

Question 27

What happens to the colliding waves after they have formed the superposition (not stationary wave)?

Answer 27

They continue along the line as normal at their original amplitude

Question 28

What must be the case for each end of a string in order for a stationary wave to form?

Answer 28

Both ends must be fixed points of 0 amplitude (nodes)

Question 29

What will happen if a string is plucked near the middle?

Answer 29

• A transverse wave travels to each end where it is reflected
• The reflected wave and incident wave superpose to give a stationary wave
• Points of 0 amplitude form at each end (nodes) and points of max amplitude fall half-way between nodes (anti-nodes)

Question 30

How do anti-nodes related the the n^th harmonic?

Answer 30

Number of anti-nodes = Number of the harmonic (n)

Question 31

What is the equation for the first harmonic and what do all components mean?

Answer 31

f₁ = (1/2L) * (T / u)^½

L - length of the string (m)

T - Tension in the string (N)

u - Mass per unit length of the string (kg/m)

Question 32

When does interference occur?

Answer 32

When two coherent waves pass through the same medium at the same time and overlap

Question 33

What are coherent sources?

Answer 33

Waves with the same frequency and a constant phase difference. (generally the same kind of wave and similar amplitudes however this isn’t part of the definition)

Question 34

What is diffraction?

Answer 34

The spreading out of waves when they pass through an opening or around an obstacle of similar size to the wavelength

Question 35

What are the features of lasers?

Answer 35

Lasers are both monochromatic and coherent

Lasers are also collimated meaning they are concentrated into a narrow beam

Question 36

What is the formula for fringe spacing and when is it used?

Answer 36

w= λD/s

ONLY USE FOR DOUBLE SLIT

w - fringe spacing (m)

λ - wavelength of light (m)

D - distance between slits and the screen (m)

s - separation of slits (m) from centre to centre

Question 37

What is meant by n^th order maximas (e.g. 1st order)?

Answer 37

The n^th order is the path difference between adjacent slits

For example, if the order number is 1, in each of the first order directions, each neighbouring slit travels 1λ further

Question 38

Explain the derivation for nλ = dsin(θ)

Answer 38

• The path difference between adjacent slits is nλ
• By drawing maxima lines, it will be obvious that for n^th order maxima, the incident light has nλ path difference from adjacent slits
• The path difference between gratings is the base of the triangle.
• d is the hypotenuse of the triangle
• Therefore, sinθ= nλ/d, so dsin(θ) = nλ

Question 39

What is a standing wave?

Answer 39

Effectively a stationary wave

Question 40

What must be the case when Young’s double slit equation to be used?

Answer 40

D must be a lot bigger than s
(small angle approximation)

Question 41

What is the wavelength of light at each end of the visible light spectrum?

Answer 41

• Red light has wavelength around 700nm
• Violet light has wavelength around 380nm

Question 42

Why are the minimas in double slit not completely dark?

Answer 42

As the rays of light travel for longer their intensity is lower this means that when the light interferes they don’t have the same intensity (as they have a path diifference). Light rays of different intensities can’t completely cancel each other out

Question 43

Are stationary waves really stationary?

Answer 43

No they just oscillate up and down (flipping) instead of left to right like a progressive wave