Module 4: Chapter 12 - Waves 2 Flashcards
What is Coherence?
Coherence is when 2 wave sources, or waves, have the same frequenecy and the same constant phase difference
What is path difference?
The difference in the distance travelled by 2 waves from their source to a specific point
What is superposition?
The overlap of 2 waves at a point in space
What is interference?
The superposition of 2 progressive waves from coherent sources to produce a resultant wave with a displacement equal to the sum of the individual displacements from the 2 waves
What is out of phase?
When 2 waves have a phase difference that is neither in phase or antiphase
When will 2 waves have a non-constant phase difference?
If the waves have different frequencies, the phase difference will be constantly changing. Therefore, sometimes they will be in phase and other times they will be out fo phase
When will constructive interference occur?
If both waves have the same sign displacement (i.e. both positive or both negative)
When will destructive interference occur?
If at the point of overlap, one of the waves has a positive displacement and the other has a negative displacement
What is reinforcement?
Constructive interference
What is cancellation?
Destructive interference
What is constructive interference?
Superposition of 2 waves in phase so that the resultant wave has a greater amplitude than the original waves (amplified wave)
What is destructive interference?
Superposition of 2 waves in antiphase so that the waves cancel each other each out and the resultant wave has a smaller amplitude than the original waves
Explain how interference patterns can form
An interference pattern can be produced from 2 coherent wave sources. Constructive interference occurs whenever the path difference between the 2 sources is a integer multiple of λ, and destructive interference occurs whenever the path difference is an integer multiple of 1/2 λ. This results in areas of constructive and destructive interference
Sketch the interference pattern for these 2 coherent wave sources:
VERY IMPORTANT
How are stationary (standing) waves formed?
When 2 progressive waves of the same frequency and amplitude travel in opposite directions. The superposition of these 2 waves forms a stationary wave
What is a node in a stationary wave?
A node is a point where the amplitude is always 0 on a stationary wave
What is a stationary (standing) wave?
A wave that remains in a constant position with no net transfer of energy and is characterised by its nodes and antinodes
What is an antinode in a standing wave?
An antinode is a point on a stationary wave that oscillates with maximum amplitude
How are stationary waves different to progressive waves?
In a progressive wave energy is transmitted, whereas in a standing wave energy is stored and there is no net transfer of energy
Draw a standing wave in an open tube (first harmonic)
Antinodes at both ends of the tube
Draw a standing wave in a tube with 1 closed end (first harmonic)
Antinode at the open end and a node at the closed end
What is the equation for wavelength in Youngs double slit experiment?
λ = ax/d
a = slit separation, x = fringe separation, d = distance between screen + slits
Youngs double slit MUST use this equation
What is the equation for wavelength in the Diffraction grating experiment?
λ = a(sinθ)/n
a = slit separation, θ = angle between incident beam and diffracted beam, n = number of fringes out
Diffractio grating MUST use this equation
What is the fringe separation if there are 10 fringes observed in 8.5mm?
9.4x10⁻⁴ m
What must you remember when determining the fringe separation
number of fringes ≠ number of spaces
What is a laser?
A laser emits a single (or close to) frequency of light
What is the phase difference between 2 successive antinodes in a standing wave?
180°
What is the phase difference between an antinode and the nearest node?
90°
What is the phase difference between an antinode and any point before the next node?
0°
between an antinode and the next node, all particles are moving in the same direction at the same time, just with a smaller displacement, thus there is no phase difference between them
What is the phase difference between an antinode and any point beyond the next node but before the antinode?
180°
Either side of the node, the particles are moving in opposite direcitons. Therefore they are antiphase and the phase difference is 180°.
2 waves of amplitude 4cm and frequency 14 Hz are moving in opposite directions at 5.6ms⁻¹ along a stretched string. The string has 2 fixed ends, a standing wave forms on this string. Determine:
a) the distance between adjacent nodes and antinodes
b) the minimum length of the string
a) 0.1m
b) 0.2 m
A wind instrument is 60cm long, and can be modelled as a tube with one closed end and one open end. What is the lowest frequency that can be played on the intrument?
137.5 Hz
A wind instrument is 60cm long, and can be modelled as a tube with one closed end and one open end. State the positions of the nodes if a note of the third-lowest frequency was played.
- One at the closed end
- One 24cm from the closed end
- One 48cm from the clsoed end
What is the first thing you should always do on a standing waves question?
SKETCH THE WAVE!
When the lowest frequency above the fundamental frequency is played, at what height will the particles’ displacement be out of phase and have the same amplitude as that of the particles 8cm above the surface of the water (0.34m depth)? The tube is 1m tall.
IMPORTANT QUESTION
0.52cm above the surface of the water
Sketch a diagram of phase difference on a standing wave relative to an antinode
What is a harmonic?
A whole number multiple of the fundamental frequency
What is the fundamental frequency?
The lowest frequency at which an object (i.e an air column in a pipe or a string fixed at both ends) can vibrate
What is the equation for slit separation?
Slit separation = 1/(number of slits per metre)
How can you create a standing wave using 1 wave source?
use the reflection of the wave to create 2 coherent waves
How can you ensure 2 loudspeakers emit coherent waves?
Connect them to the same signal generator and ensure there is the same polarity in the wires
Describe what the student would observe if they connect the microphone to an oscilloscope and move it from point A to point B
There is high amplitude in the centre between the 2 microphones. There are alternating regions of high/low amplitude as they move the microphone across. All sections of high and low amplitude are of equal width.
Describe the purpose of the single slit in this setup
To diffract the laser light and ensure 2 coherent sources from the double slit
What are 2 advantages of using a diffraciton grating to determine the wavelength of light compared with a double-slit?
- Brighter Fringes
- Fringes are spaced further apart
The first harmonic is observed with an air column of 25cm, determine the length of the air column when the next harmonic is observed
0.75 m
What is the principle of superposition of waves?
When 2 similar types of waves meet at a point, the resultant displacement at that point is equal to the sum of the displacement of the individual waves
Why can’t you produce interference patterns from filament lamps?
Filament lamps emit light of a range of different frequencies and therefore there is a constantly changing phase difference between the different waves. The light is not coherent and therefore it is not possible to produce interfence patterns
What are interference patterns?
A pattern of constructive and destructive interference formed as waves overlap. They contain a series of maxima and minima
What is a maxima in an interference pattern?
The point of greatest amplitude in an interference pattern, produced by constructive interference
What is a minima in an interference pattern?
The point of least amplitude in an interference pattern, produced by destructive interference
What did Young’s double slit experiment prove?
Light can form interference patterns, therefore it acts as a wave
What is the inter-nodal distance in terms of wavelength?
1/2 λ
Compare the amplitude of a progressive wave vs a stationary wave
- In a progressive wave, all parts of the wave have the same amplitude
- In a stationary wave, the maximum amplitude occurs at the antinode and drops to 0 at the node
Compare the phase difference in a progressive wave against a stationary wave
- In a progressive wave, the phase difference changes across one complete cycle of the wave
- In a stationary wave, all parts of the wave between a pair of nodes are in phase, and on different sides of a node they are antiphase
Sketch the first 5 harmonics on a string with 2 fixed ends
Where does a node always form in an air column and why?
At a closed end. This is because the air cannot move and therefore a node is formed
Where does an antinode always form in an air column and why?
At an open end. This is because the oscillations of air are at their greatest amplitude and therefore it must be an antinode
Explain the difference in which types of harmonics can form on a tube with 1 closed end compared to a tube 2 no closed ends.
- On a tube with one closed end, only odd numbered harmonics can form, this is because there must be a node on the closed end and an antinode on the open end. Therefore you cannot get an even multiple of the fundamental frequency as this would result in a node or antinode and both the open and closed end
- On a tube with no closed ends, all harmonics can form, this is because there must be an antinode on both ends of the column
Sketch the first 5 harmonics in a tube with one closed end
Sketch the first 5 harmonics in a tube with no closed ends
