6: Wave Behaviour Flashcards
What does the principle of superposition state?
When two or more waves overlap (superimpose), the resultant displacement equals the vector sum of the individual displacements at that position and time
Define these words
- Wavelength
- Displacement (and amplitude)
- Frequency
- Time period
- Wavelength is the distance between equivalent points on 2 consecutive waves [when distance is plotted against distance] e.g. crest-to-crest
- Displacement is the distance from the equilibrium position (Amplitude is the maximum displacement from the equilibrium position)
- Frequency is the number of complete waves passing a given point in one second.[measured in Hz]
- Time period is the time taken for a wave to completely pass through any given point. This is the reciprocal of the frequency: 1/time period = frequency & 1/frequency = time period. Note: when displacement is plotted against time, the distance between equivalent points on two consecutive waves is the ‘time period’
Interference can be [] or destructive
Constructive
What is total destructive interference?
- When a crest and a trough of equal size (amplitude), combine to give nothing. The two displacements completely cancel each other out.
- Destructive interference occurs when the two waves are pi radians or lambda/2 or 180o out of phase.
What is an example of constructive interference?
When two crests (or two trougns) from separate waves combine to create a bigger [resultant] crest (or trough).
Constructive interference occurs when the phase difference is 0o
For the interference of the waves to be noticeable, what has to be almost equal?
The amplitudes of the 2 waves
- What is phase?
- What does a phasor represent?
- Phase describes the stage of a particular point in a wave cycle
- The phase of a particular part of the wave
Phasors are rotating arrows that represent the phase of each point on a wave.
Which way does a phasor rotate?
Anticlockwise
How do you work out rate of phasor rotation?
Phasor rate of rotation is the same as the wave frequency
- What is the phase difference of waves exactly out of phase (antiphase)?
- What about their phasors?
- Phase difference is π radians [odd-numbers of π radians].
- There phasors point in opposite directions
What does ‘in phase’ mean for 2 points on a wave?
Two points on a wave are in phase if they are both at the same point in the wave cycle [e.g. crest and crest; trough and trough etc.]
Points that have a phase difference of zero or a multiple of 2π are in phase - their phasors point in the same direction
What is the phase difference of two waves emitted from an oscillator?
The waves are in phase so their phase difference is a multiple of 2π
To get clear interference patterns the two sources must be []
Coherent
- The waves must have the same frequency and wavelength.
- The wave must also have a constant phase difference between them.
What does it mean if two sources are coherent?
- They have the same wavelength and frequency
- and
- Have fixed/constant phase difference between them
What affects whether you get constructive or destructive interference at a point?
Depends on how much further one wave has travelled than the other wave to get to that point (assuming the sources are coherent and in phase)
- If the phase difference between the waves is a whole number of wavelengths, then constructive interference will take place.
- If the phase difference between the waves is an odd number of half-wavelengths, then destructive interference will take place
What is path difference?
The amount by which the path travelled by one wave from a source is different than the path travelled by the other wave from the source is called the path difference.
Describe constructive interference?
- At any point an equal distance from both sources (that are coherent and in phase), Path difference is zero
or
2.Where the path difference is a whole number of wavelengths
What is the path difference for constructive interference?
For constructive interference, the phase difference is nλ where n is an integer
What is the path difference for total destructive interference?
Destructive interference occurs when the path differnce is an odd number of half-wavelengths. e.g. (2n+1) λ/2
Describe total destructive interference
At any point where the path difference between the waves is an odd number of half wavelengths.
define standing waves
transmitted wave reflected at boundary with a 180 degrees phase change. transmitted and reflected waves superpose creating nodes and antinodes. at certain frequencies positions of nodes and antinodes are constant, resulting in a standing wave
What is a standing wave? (simple)
The superposition of two progressive waves with the same wavelength, moving in opposite directions
When do you get a standing wave?
When a progressive wave is reflected at a boundary and superposes with another wave of the same wavelength
Is energy transmitted by a standing wave?
No
What are resonant frequencies?
Frequencies where the oscillator happens to produce an exact number of waves in the time it takes for a wave to get to the end and back again, then the original and reflected waves reinforce each other
What is a node?
A position, on a standing wave, of zero amplitude
What is an anti-node?
A position, on a standing wave, of maximum amplitude
Describe the fundamental frequency
The standing wave is vibrating at the lowest possible frequency, the fundamental frequency This is the first harmonic. It has one loop with the node at each end
What is another name for the second harmonic?
The first overtone
Describe briefly standing waves on stringed instruments
They are transverse standing waves. Your finger or the bow sets the string vibrating at the point of contact. Waves are sent out in both directions and reflected back at both ends
What does a cathode ray oscilloscopes measure? What does it display?
Voltage It displays waves from an oscillator as a function of voltage over time
On a cathode ray oscilloscope, what does the vertical axis show? What does the horizontal axis show?
Vertical: voltage Horizontal: time
Describe standing waves and the wind instrument or other air column.
They are longitudinal standing waves If a source of sound is placed at the open end of a wind instrument, there will be some frequencies for which resonance occurs and a standing wave is set up Nodes form at close ends. Antinodes form at the open ends
What is refraction?
The way a wave changes direction as it enters a different medium
When does refraction occur?
When the medium a wave is travelling in changes
When a wave is refracted does the speed, wavelength, and frequency change?
The speed changes, the frequency stays constant, so the wavelength changes too