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
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?
Each loop = ½λ
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)
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!!!
When sound forms a stationary wave in a pipe, what 2 rules must it follow?
Open end(s) -> Antinode
Closed end(s) -> Node
When sound forms a stationary wave in a pipe, why can’t you use the first harmonic equation?
Sound waves cannot have a tension associated with them
When sound forms a stationary wave in a pipe closed at 1 end, what harmonics do you consider?
Odd harmonics
(n=1,3,5,…)
