What is the principle of superposition?
When two or more waves overlap at a point, the displacement at that point is equal to the sum of the displacements of the individual waves. I.e. their amplitudes combine.
How are stationary/standing waves produced?
They are produced by the superposition of two waves of the same frequency and amplitude travelling in opposite directions.
This is usually achieved by a travelling wave and its reflection. The superposition produces a wave pattern where the peaks and troughs do not move.
What are 3 ways in which stationary waves can be shown?
Stretched spring:
Vibrations caused by stationary waves on a stretched string produce sound
This is how stringed instruments, such as guitars or violins, work
This can be demonstrated by a length of string under tension fixed at one end and forced to vibrate due to an oscillators.
Microwaves:
A microwave source is placed in line with a reflecting plate and a small detector between the two
The reflector can be moved to and from the source to vary the stationary wave pattern formed
By moving the detector, it can pick up the minima (nodes) and maxima (antinodes) of the stationary wave pattern.
Air columns:
The formation of stationary waves inside an air column can be produced by sound waves
This is how musical instruments, such as clarinets and organs, work
This can be demonstrated by placing a loud speaker at the open end of an air column with fine powder inside
At certain frequencies, the powder forms evenly spaced heaps along the tube, showing where there is zero disturbance as a result of the nodes of the stationary wave.
What is an anti node (in standing waves)?
Where the vibrations are at the their maximum amplitude.
Two waves between a boundary constructively interfere.
What is a node (in standing waves)?
Where there is no vibration.
Two waves between a boundary destructively interfere.
When there are two fixed ends, what is the formula for wavelength of the nth harmonic?
nth wavelength has a wave that of 2L/n
nth harmonic has n antinodes and n+1 nodes
frequency can be calculated from:
c/lambda
State two necessary conditions for a stationary wave to be set up on a spring.
Two waves have the same frequency
Moving in opposite directions
Reflected at end of spring
With same amplitude
There is an integer number of 1/2 wavelengths between the walls
Describe the phase difference between two points on a progressive transverse wave AND a stationary wave.
Two adjacent points in a progressive wave have different phase differences.
Two adjacent points in a stationary wave with an even number of nodes in between vibrate in phase. If odd then vibrate out of phase. All points between two adjacent nodes vibrate in phase.
2 formulas needed for stationary waves wavelengths
For open-open or closed-closed:
lambda = 2L/n
For open-closed (only odd):
Lambda = 4L/(2n-1)
What is diffraction?
Diffraction is the spreading out of waves when they pass an obstruction. This obstruction is typically a narrow slit (an aperture).
What is an aperture?
A narrow slit.
Which property of a wave changes when diffraction occurs and why?
Amplitude because some energy is dissipated when a wave is diffracted through a gap.
What does the extent of diffraction depend upon.
When the wavelength is bigger than the gap, more diffraction occurs and when the wavelength is smaller than the gap, less diffraction occurs.
What is interference?
Interference occurs when waves overlap and their resultant displacement is the sum of the displacement of each wave. This is a result based on the principle of superposition. There are two types constructive and destructive. Constructive interference is when the waves are inphase (peaks and troughs of both waves lineup), and destructive when the waves are in anti phase (peak of one and trough of another lineup).
Confirm for constructive and destructive interference (formula)
Constructive:
path difference = n λ
Destructive:
path difference = (n+1/2) λ
Young’s double slit formula
λ = ax/D
λ = wavelength of source
a = distance between the centres of the slit
x = fringe width (distance between successive bright fringes)
D = distance between the slits and screen
Note all measurements in metres!
Diffraction grating formula
d sin(θ) = n λ
When are waves coherent? And give example of coherent light source and incoherent light waves
Same frequency and constant phase difference. Laser light vs filament lamp.
State 4 methods two source interference can be demonstrated and roughly explain each.
Water waves in a ripple tank
Sound
Light
Microwaves
For two source interference fringes to be observed, the sources of the wave must be
Coherent and monochromatic
What is monochromatic?
Single wavelength
State conditions required for the formation of a stationary wave.
Two waves travelling at the same speed in opposite directions overlap. Waves of the same type have the same frequency/wavelength.
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Chapter 1: Physical Quantities and Units72
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Chapter 2: Kinematics26
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Capter 3: Dynamics35
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Chapter 4: Forces, Density and Pressure28
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Chapter 5: Work, Energy And Power27
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Chapter 6: Deformation Of Solids26
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Chapter 7: Waves39
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Chapter 8: Superposition22
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Chapter 9: Electricity26
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Chapter 10: DC Circuits25
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Chapter 11: Particle Physics39
