Waves

Question 1

Define Wave

Answer 1

Wave - a periodic transfer of energy between two points without any permanent displacement of the medium

Question 2

Define Amplitude

Answer 2

Amplitude is the maximum displacement from the mean position (metres, m)

Question 3

Define Frequency

Answer 3

Frequency is the number of complete oscillations per second (hertz, Hz)

Question 4

Define Period

Answer 4

Period is the time taken for one complete oscillation (seconds, s)

Question 5

Define Speed

Answer 5

Speed is the distance travelled by a wave in one second (metres per second, ms^-1)

Question 6

Define Wavelength

Answer 6

Wavelength is the distance between two adjacent positions that are in phase (metres, m)

Question 7

Explain the whole Electromagnetic Spectrum

Answer 7

• 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

Question 8

What is the wave equation?

Answer 8

v = λ/T; v - speed; T - one period; λ - wavelength
v = fλ; f - frequency (ie period per second)
wave speed= frequency * wavelength

Question 9

Define a Longitudinal wave

Answer 9

A longitudinal wave consists of particles that oscillate parallel to the direction of propagation of the wave

Question 10

Define a Transverse wave

Answer 10

A transverse wave consists of particles that oscillate perpendicular to the direction of propagation of the wave

Question 11

How are Standing waves created?

Answer 11

Standing waves, sometimes called stationary waves, are created by the superposition of two progressive waves of equal frequency and amplitude moving in opposite directions

Question 12

Define Wave front

Answer 12

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

Question 13

Define Coherence

Answer 13

Coherence: coherent sources have the same wavelength and frequency and maintain a constant phase relationship

Question 14

Define Path difference

Answer 14

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

Question 15

Define Superposition of waves

Answer 15

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

Question 16

Define Phase of an oscillation

Answer 16

Phase of an oscillation refers to the position within a cycle that the particle occupies relative to the onset of the cycle

Question 17

How do observable interference patterns occur?

Answer 17

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

Question 18

Define Nodes and Antinodes

Answer 18

Nodes - points of zero amplitude within a standing wave

Antinodes - the points of maxima within a standing wave

Question 19

Define Fundamental frequency, Overtones, Harmonics, Timbre

Answer 19

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

Question 20

Define Refractive index and Critical angle

Answer 20

Refractive index - the ratio of the speeds in two media

Critical angle - the angle at which total internal reflection just occurs

Question 21

State Snell’s law

Answer 21

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

Question 22

Define Plane polarised waves

Answer 22

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

Question 23

Explain Photoelasticity

Answer 23

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

Question 24

Define an optically active material

Answer 24

Optically active - rotating the plane of polarisation

In sugar solutions, the angle of rotation is dependent on the concentration of the solution

Question 25

Define Diffraction

Answer 25

Diffraction - spreading of a wave passing through a gap or around an obstacle

Question 26

How is a diffraction pattern created?

Answer 26

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

Question 26

Explain the diffraction of electrons experiment

Answer 26

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

Question 27

Describe the De Broglie relation

Answer 27

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

Question 28

Using concepts such as acoustic impedance and intensity reflection coefficient explain how different media affects the transmission and reflection of waves

Answer 28

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

Question 29

Describe the pulse-echo technique:

a) Basic idea
b) Formula
c) Limitations

Answer 29

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

Question 30

Describe the Doppler effect

Answer 30

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

Question 31

Explain what determines the amount of detail in a scan

Answer 31

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.

Question 32

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)

Answer 32

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?