Chapter 12 - Waves 2 Flashcards
What is the principle of superposition
“The principle of superposition states that when 2 waves meet at a point, the resultant displacement at that point is equal to the sum of the displacements of the individual waves”
What is constructive interference
Where 2 waves superpose and are in phase and the resultant displacement is greater than the original wave
What is destructive interference
Where two waves superpose not in phase and the resultant wave has a smaller displacement than the individual waves
What are the conditions required for a constant interference pattern
and how can we remember if path or phase
- constant phase difference
- same frequency
h in coherent therefore h in phase
What happens when two waves interfere
- there are maxima where 2 waves constructively interfere
- there are minima where 2 waves destructively interfere
- maxima and minima are caused by 2 waves having different path differences by travelling different distances from their source
What are the conditions in terms of path and phase difference for waves to constructively interfere
where n is an integer:
- the path difference must be n(lambda)
- the phase difference must be 2Pi(n)
I.e the waves are in phase, there is a whole wavelength or phase separating them
What are the conditions in terms of path and phase difference for waves to destructively interfere
Where n is an integer - path difference = (n +1/2) x (lambda) - the phase difference is (2n+1)(pi) I.e. the waves are not in phase They are in antiphase
Describe an experiment to test for interference from sound
- play a sound of set frequency through 2 identical and parallel speakers
- record the intensity of the sound using a microphone as you move across the front of the speakers in a straight line
How to test for interference in microwaves and deduce wavelength
- set up 2 signal generators producing waves of constant frequency which are coherent
- move an oscilloscope across the front of the experiment and find where the first order maxima is
- measure distance from centre of first slit to first order maxima
- measure distance from centre of second slit to first order maxima
- the difference should be equal to wavelength
- repeat for other maxima and take an average
What was the importance of the evidence created by Young’s double slit experiment
- it proved the wave-like nature of light rather than particles
- if particles you would expect no diffraction thus only two bright marks directly in front of slits
- this is not what was observed
- interference patterns were observed
How to set up Young’s double slit experiment
- 2 coherent waves are required for an interference pattern
- a monochromatic light source is shone through a double slit
- onto a screen
- the monochromatic light source can be formed using a filter and a single slit
What is the formula for a double slit experiment
Lambda = ax/d Lambda is wavelength a is the slit separation x is the distance between maxima d is the distance of the screen from the slits
How does a stationary wave form
- when 2 waves of the same frequency move in opposite directions repeatedly and superpose
- they should ideally be of equal amplitude
Where are nodes and antinodes formed
- nodes are formed when the 2 waves are in antiphase and cancel out to form a stationary point of 0 amplitude
- antinodes are formed when the 2 waves are in phase and give a point of max amplitude
How to derive wavelength from a stationary wave
The wavelength is equal to twice the distance between adjacent nodes
What energy transfer occurs in a stationary wave
There is no net energy transfer, only storage of energy
What is the difference between phase difference in progressive and stationary waves
Progressive: the phase changes across a complete wave cycle
Stationary wave: all parts of a wave between nodes are in phase, by nodes they are in antiphase
Where L is the length of the string what is the wavelength of the the fundamental frequency
2L
What happens when the harmonic increases
F0 = 1 antinodes F1 = 2 antinodes F3 = 3 antinodes F4 = 4 antinodes etc.
Can a stationary wave be formed from longitudinal waves
Yes
What are the rules of stationary waves in air columns
- always antinodes at open end
- always nodes at closed ends
- From this the wavelength can be calculated
What is the equation used for calculating wavelength from a diffraction grating
n(lambda) = a sin(theta) n = order number Lambda = wavelength a = gap separation Theta = angle to maxima
define what a coherent source means
coherent sources are ones of the same frequency and constant phase difference
define path difference
the difference in the distance traveled by two separate waves or points on a wave
describe three ways stationary waves can be observed
they can be observed through
- a string of constant tension and length attached to a vibration generator
- water waves bounding off of an end wall and superposing each other
- sound waves reflecting off a wall
describe the difference in energy transfer between stationary waves and progressive waves
stationary waves simply store energy
progressive waves transfer energy from one place to another
describe the difference in wavelength between progressive and stationary waves
in a progressive wave the wavelength is the minimum distance between two parts of a wave oscillating in phase
in a stationary wave wavelength is twice the distance between adjacent nodes
describe the difference in amplitude between stationary waves and progressive waves
in progressive waves all parts of the wave have the same amplitude over the course of a wave cycle
in a stationary wave the amplitude is at its highest in the middle of an antinode and drops back to 0 at a node
define what is meant by the fundamental frequency of a wave
the lowest possible frequency for a stationary wave of a given wavelength, usually containing one antinode
how to calculate the speed of sound from a resonance tube
- hold a tuning fork above the tube and play a note
- change the length if the tube until you hear a loud resonant sound
- when the frequency of the resonant sound is equal to that of the tuning fork the length of the tube not in the water is equal to 1/4(wavelength)
- from this the speed of the wave can be calculated using the frequency of the tuning fork and 4L
graphical methods of analysing young’s double slit experiment
- if changing D, plot D (on x) against x (on y), the gradient is lambda/a
- if changing a, plot x (on y) against 1/a (on x), the gradient is lambda(D)
which direction do the particles vibrate when in a vertical air column with a stationary wave of sound
vertically
what equation including sinY can be used for double slit and diffraction gratings
sinY = lambda/ a
what equation including tanY can be used for double slit and diffraction gratings
tanY = x/d
how do these two trigonometric equations lead to the standard equation for a double slit or diffraction grating
tanY = sinY (approx) where D is much greater than a
what other use does the diffraction grating equation have
for a known angle you can calculate how many maxima are present lambda = a sinx/n thus n = a sinx/lambda n is maxima number
what is a stationary wave, define it
a stationary wave is a wave which stores but doesn’t transmit energy and is formed of a consistent pattern of nodes and antinodes caused by the interference of progressive waves travelling in opposite directions
what is a node
A node occurs where the amplitude/displacement is ALWAYS zero, caused by destructive interference from the superposition of progressive waves
what is an antinode
An antinode occurs where the amplitude of the stationary wave takes the maximum possible value, it is caused by constructive interference from the superposition of progressive waves
if we have an interference pattern created by EM or sound waves and the electrical inputs to the loudspeakers etc. are reversed what occurs to the interference pattern
- the intensities of the maxima and minima remain the same
- there remain the same number of maxima and minima
- but their positions are reversed
how can we find the wavelength of waves where there is just simple interference (as they travel in the same direction/ not stationary waves) and one speaker is moved
- set the speakers up parallel and emitting the same frequency of waves
- slowly move one speaker back until a maxima occurs on a microphone a set distance from the initial position, mark position
- continue to move the speaker back until another maxima occurs on the same microphone, mark position
- the distance between these two positions is equal to the wavelength
