Waves Flashcards
Define Wave
Wave - a periodic transfer of energy between two points without any permanent displacement of the medium
Define Amplitude
Amplitude is the maximum displacement from the mean position (metres, m)
Define Frequency
Frequency is the number of complete oscillations per second (hertz, Hz)
Define Period
Period is the time taken for one complete oscillation (seconds, s)
Define Speed
Speed is the distance travelled by a wave in one second (metres per second, ms^-1)
Define Wavelength
Wavelength is the distance between two adjacent positions that are in phase (metres, m)
Explain the whole Electromagnetic Spectrum
- Radio waves (10^3 ~ 10^-1)- wide range of frequencies allows many signals to be transmitted (radio telescopes)
- Microwaves (10^-1 ~ 10^-4) - transfer energy to water molecules in food by resonance (phones, satellites)
- Infrared (10^-3 ~ 10^-6) - radiated by warm bodies (heating, cooking, thermal imaging)
- Visible light (410^-7 ~ 710^-7) (400-700 nm)
- Ultraviolet (10^-6 ~ 10^-8) - stimulates production of vitamin D - tan (fluorescent lamps, banknotes)
- X-Rays/ gamma-rays (10^-8 ~ 10^-12) - highly penetrating, destroy tumours/less dangerous, used for diagnosis and therapy, to detect faults in metal and to study crystal structures
What is the wave equation?
v = λ/T; v - speed; T - one period; λ - wavelength
v = fλ; f - frequency (ie period per second)
wave speed= frequency * wavelength
Define a Longitudinal wave
A longitudinal wave consists of particles that oscillate parallel to the direction of propagation of the wave
Define a Transverse wave
A transverse wave consists of particles that oscillate perpendicular to the direction of propagation of the wave
How are Standing waves created?
Standing waves, sometimes called stationary waves, are created by the superposition of two progressive waves of equal frequency and amplitude moving in opposite directions
Define Wave front
Wave front is a line, or surface, in a wave, along which all the points are in phase. The distance between successive bright lines is therefore the wavelength
Define Coherence
Coherence: coherent sources have the same wavelength and frequency and maintain a constant phase relationship
Define Path difference
Path difference is the difference in distance from each source to a particular point. Positions of maximum occur when path difference is zero or a whole number of wavelengths, when the waves are always in phase and constructive superposition takes place. When the path difference is an odd half wavelength, the waves are π radians out of phase and the amplitude will be zero
Define Superposition of waves
Superposition of waves - when two waves of the same type meet (or interfere) at a point, the resultant displacement is the vector sum of the individual displacements of the waves
Define Phase of an oscillation
Phase of an oscillation refers to the position within a cycle that the particle occupies relative to the onset of the cycle
How do observable interference patterns occur?
Interference patterns - two waves combine constructively and destructively, creating a pattern of maxima and minima
Antipodal line - loud/bright; Nodal line - quiet/dark
Stable patterns only occur when:
- the waves are the same type
- the sources are coherent
- the waves have similar amplitude at the point of superposition
X = (λD)/S
X - fringe separation; D - slit to screen distance; S - slit separation
The formula only works when the fringes are close to the centre of the pattern
Define Nodes and Antinodes
Nodes - points of zero amplitude within a standing wave
Antinodes - the points of maxima within a standing wave
Define Fundamental frequency, Overtones, Harmonics, Timbre
Fundamental frequency - the frequency of the note emitted from the simplest standing wave
Overtones - the notes emitted by vibrations other than the fundamental
Harmonics - overtones that have whole number of multiples of the fundamental frequency
Timbre - quality of the note, allows us to distinguish different instruments
Define Refractive index and Critical angle
Refractive index - the ratio of the speeds in two media
Critical angle - the angle at which total internal reflection just occurs
State Snell’s law
1n2 = sin i/sin r = v1/v2; n = real depth / apparent depth
n1sin i = n2 sin r
n = 1/sin c; sin c = n1/n2
Define Plane polarised waves
Plane polarised waves are transverse waves in which the oscillations occur in a single plane that contains the direction of propagation of the wave
Longitudinal waves cannot be polarised, therefore polarisation can be a good test for transverse
Explain Photoelasticity
Photoelasticity
- we use it to look at stress patterns in solids
- different stresses rotate the plane of polarisation by different amounts
If a transparent-plastic material is placed in region X, the lines of stress can be seen when the sample is composed. The stress concentration can easily be seen. For the same stress, different wavelengths of polarised light are rotated by different amounts
Define an optically active material
Optically active - rotating the plane of polarisation
In sugar solutions, the angle of rotation is dependent on the concentration of the solution
Define Diffraction
Diffraction - spreading of a wave passing through a gap or around an obstacle
How is a diffraction pattern created?
To create a diffraction pattern using a slit, the wavelength should be of the same order of magnitude as the width of the slit
The diffraction pattern shows a central maximum edged by a series of lower intensity maxima and minima as opposed to the regular pattern of interference from a double slit. The central maximum will broaden when the slit width is reduced.
sinß = λ/a; ß - angle between central maximum and the first minimum; a - slit width
Diffraction grating - a surface with a thousand microscopic gaps, through which light can diffract
nλ=dsinß; d - slit separation; ß - angle between the central maximum and the diffracted maxima; n - the order of the maximum
Explain the diffraction of electrons experiment
Heater supply, EHT, space charge (cloud of electrons), anode, graphite sheet, vacuum, ZnS screen (fluorescent material)
We see a series of concentric rings on the screen. It is an interference pattern, it shows that electrons are behaving like waves as they are diffracted by the gaps in between the carbon atoms in the graphite and then interfering
For appreciable diffraction the gaps between the carbon atoms must be about the same size as the wavelength of the electrons
Describe the De Broglie relation
λ = h/p; λ - wavelength; h - Planck constant; p - momentum (mv)
Experimental proof of the De Broglie relation:
e*V=1/2m(v^2), so increase in V -> increase in v
so wavelength is smaller and the rings are closer together
Using concepts such as acoustic impedance and intensity reflection coefficient explain how different media affects the transmission and reflection of waves
In medicine, amplitude scans are used to determine the depth of boundaries between tissues or bone and tissue. Pulses of ultrasound are emitted by a transducer and directed into the body at the region to be investigated. A coupling gel is smeared onto the body at the point of entry so that very little ultrasound is reflected from the skin. Some of the pulse’s energy is reflected at the boundaries and received by the transducer.
The fraction of the sound that is reflected depends on the acoustic impedance of the tissue on each side of the interface. This depends on the density of the medium. The more dense, the greater the acoustic impedance.
Z = pc; Z - acoustic impedance; p - density; c - ultrasound velocity
a = Ir/Ii = (Z2-Z1)^2 / (Z2+Z1)^2; a - intensity reflection coefficient
So as the acoustic impedance of air is very small, a = 1 and everything is reflected
Describe the pulse-echo technique:
a) Basic idea
b) Formula
c) Limitations
a) The basic idea of the pulse-echo technique:
- input a value for the speed of sound/light in the material/air
- measure the time taken between sending out the pulse and receiving it back (echo)
b) v = 2x/t; as the time measured is there and back
x = vt/2
c) Limitations:
If the distance to be measured is very short (or the speed is very big) it may be that the reflected pulse arrives back before the transducer has finished emitting the pulse
Describe the Doppler effect
Doppler effect - this is an effect where the observed frequency of the waves from an approaching object is increased or from a receding object is decreased.
If the source is moving towards the observer the wavelength will be less, because the source ‘catches up’ with the waves that have already been sent out.
The speed of sound does not change. It is just that we experience more of the waves per second, so the frequency increases.
In one second the source will produce f waves (frequency = f)
These waves would occupy a distance of c metres in one second if the source was stationary (speed = c)
However, as the is moving towards the observer with speed Vs, the distance occupied by the waves is C-Vs. Therefore in one second the source produced f waves, so the distance between successive crests will be (C-Vs)/f
λf = (C-Vs)/f
Explain what determines the amount of detail in a scan
Resolution - quality of a scan - the amount of detail in it.
Resolution depends on wavelength, shorter wavelength (X-ray) gives a clearer, more detailed image, however X-ray radiation is ionising and can kill or damage cells, so ultrasound is safer.
Also resolution depends on frequency, the more frequent the better the scan. However the shorter waves are absorbed more readily and so the useful range is reduced. So for more detailed images of regions close to the skin higher frequencies are used, while the lower frequencies are used to examine the deeper organs.
Discuss the social and ethical issues (an acronym that you don’t need to know because you’ll never get asked about it but why not)
S-E-E-S
Safety - will it cause more harm than good?
Ethical - is it morally right?
Expense - do the benefits outweigh the costs?
Social - will it benefit society to adversely affect people?
