Waves 2 - Stationary Waves, Interference and Diffraction Flashcards
How do these two progressive waves interact when they overlap?
Form a superposition
Displacements combined (added or subtracted) at each point
What happens when these two pulses overlap?
Constructive interference (Displacements combine)
What happens when these two pulses overlap?
Destructive interference (Displacements cancel)
How does a stationary wave form?
- Progressive wave reflects off a fixed point
- Two progressive waves propagating in opposite directions (with same c,f,λ,A)
- Waves overlap and interfere forming superposition
- This forms areas of maximum and minimum amplitude (nodes)
On a stationary wave how are nodes and antinodes different?
Nodes → Points of 0 amplitude
Antinodes → Points of maximum amplitude
How are progressive waves different from stationary waves?
- All points on a progressive wave have same amplitude (Stationary waves have range)
- Progressive waves resultant energy transfer (Stationary waves have 0 resulatant)
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
Each loop = ½λ
Node → Node = ½ wavelength
Anti-node → Anti-node = ½ wavelength
Anti-node → Node = ¼ or ¾ wavelength
How is the frequency of the nth harmonic of a stationary wave calculated?
- Calculate the frequency of the 1st harmonic
- Multiply f1 by n
On this stationary wave why do points A and B have different amplitudes?
A and B have different maximum displacements
On this stationary wave what is the phase difference between A,B,C and D
0° → All points on same side of equilibrium are in phase
On this stationary wave what is the phase difference between A,B,C and D
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°
How can the frequency of the first harmonic on this string be decreased?
- Decrease tension (reduce mass)
- Increase distance between end points
- Use string with greater density (greater μ)
What 2 conditions are required to produce an interference pattern?
- Sources must be coherent (same frequency, constant phase difference)
- Sources must be monochromatic (one wavelength and the same wavelength)
When will two sources interfere constructively?
When their path difference = nλ
So phase difference = 0°
Maxima forms
When will two sources interfere destructively?
When their path difference = (n+½)λ
So phase difference = 180° (∏ rad or antiphase)
Minima forms
When does maximum diffraction occur?
When the wavelength is close to the size of the gap the wave passes through
What does the interference pattern of the single slit look like?
Large central maxima
Intensity decreases exponentially
Each maxima has half width of central
For the single slit how is the central maxima width affected by λ?
W ∝ λ
For the single slit how is the central maxima width affected by the gap size?
W ∝ 1/a
For the double slit, how can you increase the widths of the maximas?
- Increase λ
- Increase slit to screen distance D
- Decrease slit separation s
How does the intensity graph look for the double slit interference pattern?
Intensity decreases linearly
Width of maximas constant
How is the 1st maxima formed for the diffraction grating
between adjacent slits Path difference = 1λ
So phase difference = 0°
How is the 3rd maxima formed for the diffraction grating?
between adjacent slits Path difference = 3λ
So phase difference = 0°
How do you calculate the slit separation for a diffraction grating?
How do you calculate the maximum number of observed maximas for the diffraction grating?
nmax = d/λ
Round Down!!!
What are the requirements for superposition?
The waves must be of the same type, passing through the same medium at the same time
What happens to the colliding waves after they have formed the superposition (not stationary wave)?
They continue along the line as normal at their original amplitude
What must be the case for each end of a string in order for a stationary wave to form?
Both ends must be fixed points of 0 amplitude (nodes)
What will happen if a string is plucked near the middle?
- 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)
How do anti-nodes related the the nth harmonic?
Number of anti-nodes = Number of the harmonic (n)
What is the equation for the first harmonic and what do all components mean?
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)
When does interference occur?
When two coherent waves pass through the same medium at the same time and overlap
What are coherent sources?
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)
What is diffraction?
The spreading out of waves when they pass through an opening or around an obstacle of similar size to the wavelength
What are the features of lasers?
Lasers are both monochromatic and coherent
Lasers are also collimated meaning they are concentrated into a narrow beam
What is the formula for fringe spacing and when is it used?
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
What is meant by nth order maximas (e.g. 1st order)?
The nth 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
Explain the derivation for nλ = dsin(θ)
- The path difference between adjacent slits is nλ
- By drawing maxima lines, it will be obvious that for nth 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
What is a standing wave?
Effectively a stationary wave
What must be the case when Young’s double slit equation to be used?
D must be a lot bigger than s
(small angle approximation)
What is the wavelength of light at each end of the visible light spectrum?
- Red light has wavelength around 700nm
- Violet light has wavelength around 380nm
Why are the minimas in double slit not completely dark?
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
Are stationary waves really stationary?
No they just oscillate up and down (flipping) instead of left to right like a progressive wave
