Topic 11 - Wave phenomena Flashcards
What is the nature of standing (stationary) waves?
- An oscillating wave pattern that does not change its position
- At nodes, the displacement is always zero
- At antinodes, the amplitude is at its maximum
- Between the nodes the oscillations are all in phase
- Energy is not transferred by a standing wave
How are standing waves formed?
- Caused by interference
- The overall displacement is the sum of the two individual displacements at that moment
- Nodes occur where the two waves are always out of phase
- Antinodes occur where the two waves are perfectly in phase
What is the fundamental mode of vibration (first harmonic)?
Vibration where the wavelength is 2L (L = the length of the string)
What is the fundamental frequency, f0, of a string?
What are the wavelengths and corresponding frequencies of the harmonics?
Describe the modes of vibration on a stretched string
What is the fundamental wavelength of a pipe with open ends, closed ends, and one open and one closed end?
Both ends open = 2L
Both ends closed = 2L
One open one closed = 4L
Compare standing waves and travelling waves
What is meant by the Doppler effect?
The change of frequency that is detected when there is relative motion between a source and a receiver of waves.
What kind of waves can show Doppler effect?
Any kind
Describe the shape of wavefronts during Doppler effect
What is the equation for Doppler effect for sound for a moving source?
f’ = frequency received
us = speed of the source
v = the speed of the wave
+ if moving away from the observer
- if moving towards the observer
What is the equation for Doppler effect for sound for a moving observer?
f’ = frequency received
u0 = speed of the observer
v = the speed of the wave
+ if moving towards from the observer
- if moving away the observer
What is the equation for Doppler effect for electromagnetic waves?
v = speed between the source and the observer
Can be used if v << c
How can Doppler effect be used to measure speed?
- Radars and microwaves
Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit
How is the formula θ = λ/b for the position of the first minimum of the diffraction pattern produced at a single slit derived?
θ = λ/b → the angle for the first minimum of a single slit diffraction pattern
Sketch the variation with angle of diffraction by two point sources that has been diffracted at a single slit (resolution)
- Two sources easily resolved
- Two sources just resolved
- Two sources not resolved
What is the Rayleigh criterion?
Two points sources are just resolved if the first minimum of the diffration pattern of one occurs at the same angle as the central maximum of the other.
Apply the Rayleigh’s criterion to a picture through a narrow slit
The images of two sources can be just resolved through a narrow slit, of width b, if they have an angular separation of:
Apply the Rayleigh’s criterion to a picture through a circular aperture
The images of two sources can just be resolved through a circular aperture if they have an angular separation of:
What is the significance of resolution in radio telescopes?
- Detect wavelengths longer than visible light
- Require big diameters in order to have big resolution
What is the significante of resolution in electron microscopes?
- Electron waves are detected by a fluorescent screen or sensors
- The size of atoms is much smaller than the wavelength of visible light
- Idk the book doesn’t even say
What is the significance of resolution in digital cameras?
- The sizes of the lens and aperture affect the resolution
- Distance between the pixels must be small enough to resolve the detail provided by the lens
What is the significance of resolution in CDs and DVDs?
- The closer the lands and pits are located to each other, the greater the amounf of information that can be stored
- If the lands are too close together, the diffracting laser beam cannot resolve the difference between them → a laser with a shorter wavelength needs to be used
What is meant by polarised light?
Electromagnetic waves are (plane) polarised if all the electric field oscillations are only in one plane
What is meant by polarisation by reflection?
When unpolarised light reflects off an insulator the waves may become polarised and the plane of polarisation will be parallel to the reflecting surface (water surface etc)
What is Brewster’s law?
Used to calculate Brewster’s angle:
n = tan*ϕ *
What is Brewster’s angle?
The angle at which all of the reflected light is polarised = when the refracted rays and the reflected rays are exactly at 90° angle to each other
What is a polariser?
A special filter that is used to convert unpolarised light into polarised light by absorbing oscillations in all planes except one
What is an analyser?
A second filter used after a polariser, which can be rotated to analyse light to determine if it is polarised and in which direction
What is Malus’ law?
I = I0cos2θ
What is an optically active substance?
A substance which rotates the plane of polarisation of light waves passing through it.
How can polarisation be used to determine the concentration of certain solution?
The greater the concentration of an optically active substance, the more the plane of polarisation is rotated.
How can polarisation be used in stress analysis?
- Some plastics ang glasses become optically active and rotate the plane of polarisation of light when they are stressed
- The greater the stress, the greater the rotation of the plane of polarisation
- A transparent material is placed between polarising filters and put under the action of various forces
Outline the function of liquid-crystal displays (LCD)
- A liquid crystal is a state of matter that has physical properties between a liquid and a solid
- The ability to polarise can be changed by applying a small potential difference
- If there is no p.d., no light is transmitted out of the analyser
- When a p.d. is applied, its molecules change orientation
- The plane of polarisation rotates and some or all of the light is transmitted
- The amount of rotation and the amount of light transmitted depend on the size of the p.d.
- In displays, light entering through the front passes through the liquid crystals and is then reflected back to the viewer
- Each segment of the display will appear dark or light, depending whether a p.d. has been applied
