5.2 - The Behaviour Of Waves Flashcards
What’s the wave phase
All points on a wave will be at some position through their cycle of oscillation, some positions have their own names eg peak, crest, rarefaction or compression
We describe any position through a cycle by a number, referred to as the phase
What is a complete cycle or a wave equal to
It’s considered equivalent to rotation through a complete circle - so the phase position will be an angle measurement, where a complete cycle is equal to 360 degrees
What’s the alternative angle units to degrees
Radians
What’s one cycle equal to in raisins
One cycle is 2 pi radians
Radians can be shortened to rad
What are wavefronts
Diagrams of waves are often drawn as lines, where all the points in a line represent points on the wave that are exactly the same phase position, perhaps a wave crest for example
These lines on a diagram are call wavefronts
What is a ray on a wave diagram
The line showing the direction of travel is called a ray, rays must be perpendicular to wavefronts
What happens with wave superposition
When waves meet, each wave will be trying to cause a displacement at that point of intersection, according to its phase at that location. The net effect is that the overall displacement will be the vector sum of the displacements caused by the individual waves
After the encounter, each wave will continue past eachother, as the energy progresses in the same direction it was originally travelling - this can be simply illustrated if we consider just wave pulses passing each other - waves go back to original displacement after the intersection
What happens with the superposition of continuous waves
If rather than a single point along the path of the waves, we consider waves superposing over an extended space, the outcome is a continuous wave that is the sum of the displacements over time in each location
What’s constructive interference
If the two continuous waves are in phase, their effect will be to produce a larger amplitude resultant wave
What’s destructive interference
If identical waves meet and are exaclty out of phase, phase difference is 180 degrees, then the resultant is a zero amplitude wave
Define wavefronts
Wavefronts are lines connecting points on the wave that are at exaclty the same phase position
Define constructive interference
It’s the superposition effect of two waves that are in phase, producing a larger amplitude resultant wave
Define destructive interference
It’s the superposition effect of two waves that are out of phase, producing a smaller amplitude resultant wave
How can a stationary or standing wave be set up
Continuous waves travelling in the opposite directions will superpose continuously, this can set up a standing wave.
The waves need to be if the same speed and frequency with similar amplitudes and have a constant phase relationship
What’s coherent
Waves with the same frequency and a constant phase relationship are said to be coherent
Thus waves must be coherent in order for a standing wave to occur
What do stationary waves do
They are so called stationary waves as the profile of the wave does not move along, it only oscillates. This also means that wave energy doesn’t pass along a standing wave - they kind of don’t meet definition of waves, which do transfer energy and are more precisely called progressive waves
What are progressive waves
Waves that transfer energy
What are nodes and antibodies
On a standing wave,
Nodes are the points where the resultant displacement is always zero, thus points never move
Antibodies are points of maximum amplitudes
All points between one node and the next are In the same phase at all times although their amplitude of vibration varies up to the antipode and back to zero at the next node
This can be demonstrated in school, with a vibration generator and a rubber cord
At the end points on a stationary wave what happen
If the string / wave thing is fixed at each end, these points must always be nodes!!!
A standing wave can only occur if its wavelength exaclty allows one node at each end
Tell me about
U
What are modes of a stationary wave
They are harmonics - pls search up a pic so you understand
There are a quanised (limited/finite) number of half wavelengths that a standing wave can have as the fixed ends of the waves must be nodes
List the different modes
Fundamental (1st harmonic) wavelength is equal to 2L
Then it’s the 1st overtune (2nd harmonic) and wavelength is equal to L
Then the 2nd overtune (3rd harmonic) and wavelength is equal to 2L/3
And 3rd overtune (fourth harmonic) where wavelength is L/2
How do string waves travel
Waves on a stretched string travel at a speed that is affected by the tension in the spring(newtons) and the mass per unit length of the string, weird u symbol in kg/m
What’s the equation for the speed of a wave In a string
V = square root T/ weird u
T = tension u = mass per unit length V = speed
How can the wave speed equation for a string be combined with the wave equation
V = f x lamder
F x lamder = square root T/weird u
F = 1/lamder x square root T/u
In the fundamental mode of vibration(first harmonic), fundamental frequency, f subscript 0, depends on the length of the string, tension and mass per unit length from
F subscript 0 = 1/2L x square root T/u
How can we investigate the factors affecting fundamental frequency of a string
We can verify the equation
F subscript 0 = 1/2L x square root T/u Experimentally.
Need to undertake 3 separate investigations to verify each part of the relationship, whilst maintaining other variables as control variables
So need to verify
F0is proportional to 1/L
F0 is proportional to square root T
F0 is proportional to square root 1/u
We can use a microphone connected to an oscilloscope to monitor the sounds produced by a sonometer string and to measure its frequency of vibration . This can be easier if a datalogging computer is used instead of an oscilloscope, so the screen can be frozen fir close scrutiny
1) the string supports (bridges) on a sonometer are moveable, so that we can find the frequency with varying lengths, L whilst the same string (constant u) and hanging masses (T) keep the other variables controlled. We can plot a graph to verify f0 on the y axis is proportional tO 1/L on x axis
2) we can find the fundamental frequency using a fixed length of the same string throughout (constant L and constant u) for varying masses hung over the pulley - varying T. We can plot a graph to verify f0 on the y axis is proportional to square root T on the x axis
3) the final experiment requires a set of different strings (varying diameter metal wires could be used). Maintaining the same length and hanging mass keeps other variables controlled. Measure the mass of each wire using a digital balance and its full length, In order to calculate mass per unit length, u, for each wire or string used - we can plot a graph to verify f0 on the y axis is proportional to square root 1/ u on the x axis
Define a stationary or standing wave
Consists of oscillation in a fixed space, with regions of significant oscillation and regions with zero oscillation, which remain in the same locations at all times
When are waves said to be coherent
If they have the same frequency and have a constant phase relationship. Coherent waves are needed to form a stable standing Wave
What’s a progressive wave
Is a means of transferring energy via oscillations
What are nodes
Nodes are regions on a stationary wave where the amplitude of oscillation is zero
What are antinodes
Are regions on a stationary wave where the amplitude of oscillation is at its maximum
What’s a sonometer
A sonometer is an apparatus for experimenting with the frequency relationships of a string under tension, usually consisting of a horizontal wooden sounding box and a metal wire stretched along the top of the box
How does diffraction change with objects
When a wave passes the edge of an obstacle, the wave energy spreads into the space behind the obstacle. If the obstacle is relatively small, this can mean wave energy will pass around both sides of it and continue travelling past the obstacle with no shadow, as if the obstacle was not there
If the obstacle is larger, then there may be a shadow region behind it, but there will still be some diffraction around the edge
If there are two close obstacles forming a gap, then there will be diffraction from each edge of the gap, causing the waves to spread out through the gap
What is diffraction
Diffraction is a spreading of wave energy through a gap or around an obstacle
What are 2 factors affecting diffraction for obstacles
The amount of diffraction around an obstacle depends on the size comparison between the obstacle and the wavelength
How does the gap size affect diffraction
As the resulting diffraction through a gap is caused by the diffraction at each end of the gap, there is an optimum size for maximum diffraction, or spreading out through the gap.
Diffraction happens most when the gap size is the same as the wavelength. If the gap size is too small, very little wave energy can pass through. If the gap is very large, there is little effect as the majority of the wave passes through undisturbed.
When the wavelength matches the gap size, the wave energy is spread very effectively through the gap to fill the space behind. This is why we can hear around corners but not see around them - audible sound wavelength much larger so math more the gap of a doorway.
What are diffraction patterns observed when light passes through a narrow slit
The pattern shows a central maximum and then areas of darkness and further maxima of decreasing intensity,
Eg using a laser with a diffraction grating with slits shows an example of an interference pattern
Considering the waves being diffracted from each end of the slit, gives us two waves that will meet at the screen, they superpose to give a larger amplitude resultant wave and so would appear as a light spot on the screen
At a differnt place on the screen, these two waves will be completely out of phase and the sum of their displacements will always be zero, so it appears as a dark spot - the diffraction pattern is an example of a standing wave on the screen, where there are dark spots of nodes and light spots of antinodes
What happens when we alter the slit (single slit) to diffraction
If we change the width of diffraction slit, we will alter the diffraction pattern that we observe
A narrower slit widens the central maximum, as well as the further maxima and minima
What is a diffraction grating
A diffraction grating is a device that will cause multiple diffraction patterns, which overlap creating an interference pattern with a mathematically well defined spacing between bright and dark spots, it is a collection of a very large number is slits through which the waves can pass. These slits are parallel and have a fixed distance between each slit - can be used to examine line spectra
What equation does the pattern produced by each colour passing through a diffraction grating follow
n lamder = d x sin theta
Where theta is angle between the original direction of the waves and the direction of the bright spot
Lamder is the wavelength of the light used
d is the spacing between the slits on the grating
n is the order. The order is the bright spot number from the central maximum which n = 0
The grating spacing is often quoted as a number of lines per metre, so to find d
You do d = 1/ number per meter
How can we investigate diffraction with a laser practical
You can use a laser pointer or laboratory experimental laser to demonstrate diffraction. A diffraction grating investigation allows careful study of the light making up the spectrum from any light source
Astronomers use this to study spectra from stars
Diffraction gratings are manufactured to have a fixed spacing, d, between lines on the grating, and this will be printed on the grating. By measuring the angle between each maximum brightness spot created by a diffraction grating, you can calculate the wavelength of the light used from the diffraction grating equation
What is an interference pattern also known as
When a wave meets its own reflection, it would set up a standing wave pattern, also known as an interference pattern.
Reflection is a convenient way to generate coherent waves that will produce a standing wave. However any combination of waves that have the same frequency and a constant phase relationship will produce this result
Tell me about two slit interference / where Thomas young got his wave theory of light
Using a forth and two slits to make 2 coherent waves that produce a standing wave pattern, that showed a pattern of dark and light fringes that resemble the nodes and antinodes in a standing wave
Young explained his experiment that light behaves as a wave, since in classical physics interference can only occur with waves - theory was controversial at the time as it was contradicting Newton’s theory that light was a steady stream of particles
How can we investigate two- source interference
A ripple tank where plane waves are diffracted through two gaps will cause an interference pattern between the two water waves
Another common experimental demonstration of two slit interference is with a last light
Two source interference and two slit interference are the same thing, waves are brought together to produce an interference pattern.
Two slit interference is a form of two source interference, where the slit diffract existing waves in order to act as new sources of waves
How can we explain two slit interference
Each point in a two source interference pattern will have a superposition result that depends on the phase difference between the waves coming from each source to that point. Phase difference, will in turn, depend on the relative distances from the slit to where they meet
If waves meet on the screen, the waves will constructively interfere and produce a maximum resultant as in an antinodes, if we passed a laser through the 2 slits, there would be a bright spot there
How can we compare and thus convert to phase difference between waves
Points where the path difference is equal to n lamder exactly will have a phase difference of 2n pi exaclty and will be In phase, producing constructive interference
Points where the path difference is equal to (2n+1)xlamder all divided by 2 will have a phase difference of (2n+1) lamder and will be in antiphase, producing destructive interference.
Define interference
It’s the superposition outcome of a combination of waves. An interference pattern will only be observed under certain conditions, such as waves being coherent
What are coherent waves
Waves must have
The same frequency
Constant phase relationship
