Chapter 12- Waves 2 Flashcards
When does superposition happen?
When two waves of the same type meet, either because they are going in opposite directions or one overtakes the other
They continue as they were otherwise
Principle of superposition
When two waves meet at a point, the resultant displacement at that point is equal to the sum of the displacements of the individual waves
Constructive interference
When the two waves are exactly in phase, the combined wave has an amplitude equal to the sum of the amplitude of each
Destructive interference
When two waves are in anti-phase, the waves cancel each other out so the resultant displacement is 0m
Coherence
The waves have the same frequency and constant phase difference so the interference pattern will be regular
Path difference
The difference in the distances travelled by the waves
Path difference -> phase difference
Replace λ with π and double the coefficient
Node vs anti-node
In a standing wave, a node has 0 displacement and an anti-node maximum displacement
1st order minima
π or λ/2
1st order maxima
2π or λ
Path difference at a maxima
nλ
The waves are in phase
Path difference at a minima
(2n-1)λ/2
The waves are in anti-phase
Stationary waves
Produced by superposition of two progressive waves of equal amplitude and frequency, travelling with the same speed in opposite directions.
Stationary wave characteristics
Varying amplitude
Doesn’t transfer energy
In phase between nodes, in anti-phase either side of one
Young’s Double slit experiment
Pass an incoherent light source through a single slit or use a coherent light source
Then put a double slit in front with a screen a large distance behind
Young’s Double slit wavelength equation
ax
λ = ——–
D
Where a is the distance between the slits, x the distance between the first and second maxima and D from the double slit to the screen
Why does Young’s double slit experiment produce that pattern?
It passes a coherent wave through a double slit which causes it to diffract
Where the path difference is an integer coefficient of the wavelength there will be constructive interference and a maxima
Distance between a neighbouring node and anti-node in a standing wave
λ/4
Standing waves on strings
They have a fixed point at either end so there will be a node at each end
Amount of nodes in the 2nd harmonic
1 in between the two at the end
Amount of nodes in the 3rd harmonic
2 in between the two at the end, it increases by 1 each time
Fundamental frequency
f0, the minimum frequency of a stationary wave of a harmonic, produces the 1st harmonic with no nodes in the middle
Finding the wavelength from a harmonic
λ = 2L/n
Where b is the harmonic number, and L the length of the string
Frequency of a harmonic
f = n(f0)
Where n is the harmonic number
Stationary wave vs progressive waves
- progressive waves transfer energy through space, standing do not
- phase varies constantly along a progressive wave, in a standing wave all points between two nodes are in phase
- the frequency/wavelength of a standing wave is equal to that of the progressive waves that form it
What affects the pitch of a sound?
Tension
Length of string
Thickness of string
Nodes and anti-nodes on a longitudinal standing wave
They are in terms of the displacement of particles, nodes on a longitudinal wave are where particles arent moving
Standing waves on tubes
There is always a node at a closed end and an anti-node at an open end
Fraction of a wavelength in a tube with two open ends
n λ
——-
2
Where n is the harmonic number
Fraction of a wave in a tube with one open and one closed end
(2n-1) λ
———
4
Where n is the harmonic number
Phase in standing waves
Points are in phase if they are between 2 nodes
