6: Wave Behaviour Flashcards
When does superposition happen?
When two or more waves pass through each other
What happens when two waves superpose?
At the instant the waves cross, the displacements due to each wave combine. Then each wave carries on.
What does the principle of superposition state?
When two or more waves cross, the resultant displacement equals the vector sum of the individual displacements
Interference can be [ ] or destructive
Constructive
What is total destructive interference?
When a crest and a trough of equal size, combine to give nothing
What is an example of constructive interference?
When two crests combine to create a bigger crest
For the interference of the waves to be noticeable, what has to be almost equal?
The amplitudes of the 2 waves
What does a phasor represent?
The phase of the wave
Which way does a phasor rotate?
Anticlockwise
What does ‘in phase’ mean?
Two points on a wave are in phase if they are both at the same point in the wave cycle
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 waves exactly out of phase (antiphase)? What about their phasors?
Phase difference of odd-numbers of π radians. There phasors point in opposite directions
What is the phase difference of two waves emitted from an oscillator?
They are in phase so their phase difference is a multiple of 2π
To get clear interference patterns the two sources must be [ ]
coherent
What does it mean if two sources are coherent?
They have the same wavelength and frequency and a fixed 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)
What is path difference?
The amount by which the path travelled by one wave is longer than the path travelled by the other wave is called the path difference
Describe constructive interference
At any point an equal distance from both sources (that are coherent and in phase), or where the path difference is a whole number of wavelengths
What is the path difference for constructive interference?
nλ where n is an integer
Describe total destructive interference
At any point where the path difference is an odd number of half wavelengths
What is the path difference for total destructive interference?
(2n+1) λ/2
How can you observe interference with soundwaves?
Connect two speakers to the same oscillator, so they are coherent and in phase, and place them in line with each other
Slowly move the microphone in a straight line parallel to the line of the speakers
Using a datalogger and a computer, you can see where the sound is loudest and quietest – the locations of maximum constructive and destructive interference
What is a standing wave?
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
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
Describe how you would investigate standing waves using a string
Take a piece of string and fix it in place at one end
Attach the other end to an oscillator
Adjust the frequency of the oscillator until a standing wave is formed
You can then use an oscilloscope to calculate the resonant frequency
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 resonant 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 does the gain dial do on a cathode ray of oscilloscope?
It controls the voltage represented by each division
What does the timebase dial control on a cathode ray oscilloscope?
The time represented by each division
How do you work out the frequency of a wave on a cathode ray oscilloscopes?
Find the time period by counting how many horizontal squares one wavelength covers. Multiply that number by the time base value you set on the oscilloscopic. Use this to calculate the frequency of the waves being generated by the oscillator
How can you create a resonance tube?
Place a hollow tube into a measuring cylinder of water