Chapter 4 - Waves Flashcards
What’s is mean position of a wave?
It’s the fixed average point of the particles of the wave
Amplitude
The maximum displacement from the mean position
Frequency
Number of oscillations completed in one second
Unit: Hz
Time period
Time taken for one complete oscillation
Phase difference
Measures in degrees or radians, how ‘in step’ the different molecules are
In phase: moving together
Out of phase: moving separately
What’s one complete cycle and half a cycle?
360 degrees/2 Pi = one complete cycle
Pi = half a cycle
90 degrees/ Pi/2 = quarter of a cycle
Continuous wave
Involves a succession of individual oscillations
A wave pulse
Involves just one oscillation
Longitudinal waves and examples
Oscillations are parallel to the direction of energy transfer.
E.g sound waves and earthquake waves
Transverse waves and examples
Oscillations are perpendicular to the direction of energy transfer
E.g light waves, water ripples and earthquake waves.
Transverse mechanical waves cannot be propagated through fluids.
Wave equations
Wave speed (velocity) = frequency x wavelength
Displacement
Measures the change that has taken place as a result of a wave passing a particular point.
Zero displacement refers to the mean position
Wave speed
The speed at which the wave fronts pass a stationary observer.
Symbol: c
Unit: ms^-1
Intensity
Power per unit area that is received by the observer
Unit p: Wm^-2
Intensity is proportional to the square of its amplitude
What is the electromagnetic spectrum and its properties?
Gamma rays, x-rays, UV, visible, IR, microwaves and radio waves.
All transverse waves, can travel through a vacuum. All have the same speed 3.0 x 10^8 ms^-1
How are magnetic fields involved with the electromagnetic spectrum?
Accelerating charges generate electromagnetic fields. If a a electric charge oscillates it will produce a varying electric and magnetic field perpendicular to one another.
What is interference?
When two of the same type of wave meet. It can take place if there are 2 possible routes for a ray to travel from source to observer.
A resultant wave is the 2 waves added together
After the 2 waves meet they travel unaffected by their meeting.
When can there be areas of constructive or destructive?
If the waves have the same amplitude and frequency then the interference at a particular point can be constructive/ destructive.
What is constructive interference?
When the two waves are in phase and are always adding up. There is zero phase difference.
Path difference = n wavelength
What is destructive interference?
Takes place when the waves are out of phase. E.g the phase difference is half a cycle, or 180 degrees, or Pi radians
Path difference = (n + 1/2) wavelength
What is a phase change?
It’s when a trough comes back as a peak (the wave is flipped)
What’s a path difference?
The extra physical distance one wave might of gone that the other one didn’t.
What’s coherent?
The 2 waves have a constant phase relationship (but don’t have to be in phase) as the sources are constantly producing them. The frequency must be the same and stay that way.
What’s non-coherent?
Phase change occurs because waves aren’t continuously being produced.
The plane of vibration of an electromagnetic wave
The plane that contains the electric field and the direction of the propagation.
Polarised light
Over a period of time, the electric field only oscillates in one direction.
Unpolarised light
Over a period time, the electric field oscillates in random directions.
What is partially plane-polarised and circularly polarised?
1) . A mixture of polarised light and unpolarised light.
2) . If the plane of polarisation rotates uniformly
What is a polariser?
Any device that produces plane-polarised light from an unpolarised beam.
What is an analyser?
It’s a polarised used to detect polarised light.
What is a Polaroid?
A material which absorbs any light in one particular plane of polarisation allowing transmissions only in the plane of 90 degrees to this.
What is Brewster’s Law?
The reflected ray of a light Ray is always partially plane-polarised. If the reflected ray and the refracted Ray are 90 degrees to each other than the reflected ray is totally plane-polarised.
The angle of incidence for this condition = polarising angle
What’s the equation for Brewster’s Law?
n (the refractive index of the medium) = tan i (i = polarisation angle)
What’s the difference in what light sources emit compared to radio, radar and laboratory microwaves emit?
Radio waves etc.. Often emit plane-polarised light whereas light waves do not. Light can be polarised as a result of reflection and selective absorption.
How are crystals involved with polarisation?
Some crystals exhibit double refraction or birefringence; where in polarised light rays enter the crystal and is split into two plane-polarised beams that have mutually perpendicular planes of polarisation. This is because they refract differently as they travel at different speeds.
What is Malus’s Law?
The intensity of light is proportional to the (amplitude)^2 ( how intensity varies with the angle)
I = I (o) x cos^2 (angle)
I = transmitted intensity of light in Wm^-2 I(o) = incident intensity of light in Wm^-2 Angle = angle between the plane of vibration and the analyser's preferred direction.
How is the material Polaroid constructed?
It has a long chain of molecules which selectively absorb light that has electric fields aligned with the molecules.
How to Polaroid dark glasses work (sunglasses).
It allows light with vertically oscillating electric fields to be transmitted and absorb light with horizontally oscillating electric fields.
What effect do the Polaroid dark glasses work overall?
Overall light intensity and ‘glare’ from horizontal surfaces will be reduced.
Light reflected from horizontal surfaces will be horizontally plane-polarised to some extent.
What happens when glass and some plastics are placed under stressed?
The stress comes from the molecules being twisted or stretched.
They become birefringent. Bright coloured lines are observed in regions of maximum stress when white light is polarised and passed through stressed plastic.
What is birefringence?
When an objects refractive index depends on the polarization and propagation direction of light. It’s the rotated polarised direction and the two components are slowed
What is an optically active substance?
It rotates the plane of polarisation of light that passes through it.
E.g sugar solution. The more concentrated the solution, the more molecules the oscillations meets and the greater it rotates.
What are Liquid-Crystal Displays (LCDs) and what does is do?
E.g calculator displays and computer monitors
The liquid crystal is sandwiched between 2 glass electrodes and is birefringent. The crystal has a twisted structure and causes the plane of polarisation to rotate through 90°. Thus, light can pass through the second polariser, reach the reflecting surface and be transmitted back along the original direction.
How is potential difference related to LCDs?
With no pd across the electrodes, the LCD appears light.
With a pd, it causes molecules to align with the electric field. So less light is transmitted and this section of the LCD will appear darker.
How do LCDs use coloured filters?
It’s used to create a colour image.
What would occur if there was no liquid crystal between the electrodes?
The second polariser would absorb all the light passed through the first one, and the screen would appear black.
What type of waves can be polarised?
Transverse waves
What happens when a wave meets the boundary between two different medias?
It’s partially reflected and partially transmitted.
What’s the law of reflection?
Angle of incidence = angle of reflection
Both the rays lie on the same plane.
What is perfect reflection?
When a single ray of light strikes a smooth mirror it produces a single reflected ray.
What is diffuse reflection?
When a single incident ray hits an uneven surface the reflected rays go in different directions. Objects become visible with a source of light because diffuse reflections have taken place that Scatter light from the source to our eyes.
What is a ray and how are they drawn?
It’s a line showing the direction in which light energy is propagated. It must be at right angles to the wavefront.
Refraction
Occurs at the boundary between 2 medias. The wave will undergo a change of direction due to a change of wave speed.
What happens the the refraction of the wave depending on the density of the second median?
If a ray travels into a denser medium, it refracts towards the normal.
If a Ray travels into a less dense medium, it refracts away from the normal.
Equation for snell’s law (the refractive index)
Sin i/ sin r = n
n = constant, for a given frequency.
What is the refractive index for air?
n = 1.0
What ps the relationship between the refractive index and the wave speed?
The ratio is equal to the ratio of the speeds in the different media
n(1)/n(2) = sin (o)(2)/ sin (o)(1) = V(2)/V(1) V(2)= speed of wave in medium 2 V(1)= speed of wave in medium 1
What’s the critical angle?
Critical ray: the ray which has a refracted angle of 90°.
Critical angle: angle of incidence for the critical ray
What happens if the angle of incidence is greater than the critical angle?
Refraction cannot occur so the ray is totally internally reflected at the the boundary and stays in the same medium of which it came from.
Equation for the critical angle:
Sin(0c) = 1/n Sin(0c) = critical angle
Diffraction
When a wave passes through apertures they spread out, and they also spread around obstacles
When does diffraction become more important?
When the wavelength is large in comparison to the size of the aperture.
The wavelength needs to be the same order of magnitude as the aperture for the diffraction to be noticeable .
What happens to the intensity of the maximas as the angle increases?
The intensity decreases
What is two source interference?
It’s another application of superposition, for 2 coherent sources having roughly the same amplitude. Within the areas of interference there is constructive and destructive interference, and sections of maximas and minimas.
Young’s double slit interference
A monochromatic light source (only gives out one frequency), and the light from the twin slits interferes and patten of light and dark regions (fringes) are seen on the screen.
What’s the equation for the double slit experiment: angles of the maxima?
n x wavelength = d sin(0)
n = number of maxima d = distance of the slits
We can ignore the sin, but only if it’s in radians and the angle is very small
What’s the equation for the fringe separation (how far apart the area of brightness are)/ how far apart the maximas are?
s = wavelength x D / d D = distance of light source to screen
What is the difference of the maxmias and the minimas?
Maxima: waves are in phase
Minima: waves are out of phase and cancel out, thus the dark areas.
When will a standing wave be formed?
When 2 waves are:
Of the same amplitude and frequency
travelling in opposite direction
What’s the most often situation standing waves occur?
When a wave reflects back from a boundary along the route it came. The reflected wave and the incident wave are (nearly) equal amplitude, so they interfere.
Features of Nodes
Areas of destructive waves, the waves always cancel each other out; they have no amplitude.
Features of antinodes
Areas of constructive interference. The amplitude is 2A (twice the amplitude of the old wave, as now we add both together). It’s the maximum displacement.
What’s the amplitude of each point in a standing wave?
All points have the same amplitude - at some point during the wave, the single point will reach the maximum and minimum displacement.
Does standing waves transmit energy?
Energy isn’t transmitted, but does have energy associated by it.
What’s the phase and the wavelength of a standing wave?
All points between one node and next one are moving in phase.
The wavelength is twice the distance from one node (or antinode) to the next node (or antinode).
What’s the boundary range?
What a wave can/can’t do.
Specifies the condition that must be met at the edges of the system when standing waves are taking place.
What types of waves can a standing wave be produced from?
Longitudinal and transverse.
Closed ended pipe
Molecules at an open end must be at a pressure node because the outside of the pipe is at a constant (atmospheric) pressure. However, they are free to move, thus they are at a displacement antinode.
The molecules at the closed end of a pipe are at a displacement node because they cannot move past the end of the pipe. However, they still feel the wave from the rest of the pipe which will alternately squash them against the solid end, and pull them away: thus they are at a pressure antinode.
