Considering the relationship shown for velocity in SHM, describe the conditions when the velocity is at a maximum and at a minimum.
Velocity is at a MAXIMUM when y = 0 (This simplifies the equation to v_{max}=ωA).
Velocity is at a MINIMUM (zero) when y = A or A.
Assuming no energy losses, describe how the type of energy an object undergoing simple harmonic motion has changes over time.
The energy of the object is constantly being converted from kinetic energy to potential energy and back again.
Kinetic energy is at a maximum when velocity is at a maximum (at y=0).
Potential energy is at a maximum when velocity is zero (when y = A or A)
At any point:
total energy = potential energy + kinetic energy.
Classical theory suggested that as an object becomes hotter, the irradiance of short wavelength radiation would increase dramatically. In fact, experiements show this irradiance is very small.
What is this effect known as, and why does it happen?.
 This is known as the 'ultraviolet catastrophe'.
 The reason it happens is because individual photons have their energy quantised by the relationship E=hf.
 Due to energy conservation, there are far less high energy photons allowed than at other wavelengths.
The direction of the force exerted on a negatively charged particle entering a magnetic field perpendicularly can be determined using the 'right hand rule'.
Describe the use of the 'right hand rule' by determining which 'finger' represents which quantity.
State the Heisenberg uncertainty principle.
Heisenberg’s uncertainty principle states that the precise position of a quantum particle and it's momentum cannot both be known at the same instant.
The de Broglie wavelength of a particle can be considered to be the same as the uncertainty in its position (Δx).
Considering this, explain what conditions are required to create diffraction patterns from beams of particles by a double slit.
The distance between the slits needs to be approximately equal to, or smaller than, the particle's de Broglie wavelength, as there is an uncertainty to which slit the particle will travel through.
If the slits are a greater distance apart, the particles will only pass through one slit and no diffraction pattern will be observed.
State what is meant by an object undergoing 'simple harmonic motion'.
The restoring force (on the object) is directly proportional to, but opposite in direction to, the object's displacement from its equilibrium position.
Describe the motion of a charged particle which enters a magnetic field:
 Perpendicular to the field
 Parallel to the field
 At an angle
 The particle will travel with circular motion only.
 The particle will continue with linear motion parallel to the field only.
 The particle will travel with helical motion (circular perpendicular to the field and linear parallel to the field).
By referring to the uncertainty principle relating energy and time, explain the concept of 'quantum tunneling'.
the lifetime of a particle may be sufficiently short for the uncertainty in its energy to give a realistic probability of the particle having sufficient energy to escape from the potential well
or
(particle can) ‘borrow energy’ for a short period of time (to escape from the potential well)
Explain the production of 'cosmic air showers' when cosmic rays enter the atmosphere.
The cosmic ray strikes a nucleus creating secondary particles (usually hadrons such as the pion) which in turn collide with other particles and so on creating a 'shower' of particles which are detectable a ground level (such as muons, positrons and neutrinos).
'Cosmic air showers' provided the very first evidence for sub nuclear particles and the quark model of matter.
Assuming the relationship
y = A sin ωt
derive expressions for velocity and acceleration for an object undergoing simple harmonic motion.
y = A sin ωt
differentiating this gives
v = Aω cos ωt
differentating this again gives
a = Aω^{2} sin ωt
= ω^{2}y
State what is meant by 'cosmic rays'.
Cosmic rays are high energy particles entering the atmosphere from space.
They consist mainly of protons, electrons and alpha partciles from the sun, known as the solar wind.
Neils Bohr and Louis de Broglie suggested that electrons can be considered as 'standing waves' in orbit around the nucleus of an atom.
Using the circumference of an orbit (2πr) being equal to n de Broglie wavelengths (nλ), derive an expression for the quantised angular momentum of an electron.
2πr = nλ
2πr = nh/p (since λ = h/p)
2πr = nh/mv (since p = mv)
mvr = nh/2π
A stationary wave is formed in a piece of elastic string under tension, created by a vibration generator set to 250Hz as shown below.
The distance between adjacent nodes is 0.15m
 Determine the wavelength of this wave.
 Determine the speed of this wave.
 The wavelength of the wave is 0.3m (The distance between nodes is equal to half a wavelength).
 The speed of the wave = frequency x wavelength
= 250 x 0.3
= 75 ms^{1}
The magnitude of the force on a charged particle entering a magnetic field can be determined using the relationship
F = qvB
where v is the particle's velocity perpendicular to the magnetic field, B.
How should you deal with particles that do not enter fields perpendicularly?
You should calculate the component of the particle's velocity perpendicular to the field.
In this example, v would become vsinθ
What is the relationship between the energy transferred by a wave and the amplitude of the wave?
The energy transferred by a wave is proportional to the ampltude squared of the wave.
E = kA^{2}
or
E_{1}A_{1}^{2 }= E_{2}A_{2}^{2}
Starting with the relationships
y = A sin ωt and v = Aω cos ωt
show that the velocity of a particle undergoing simple harmonic motion can be expressed as
 y = A sin ωt and v = Aω cos ωt
rearranging gives
 sin ωt = y/A and cos ωt = v/Aω
since sin^{2}ωt + cos^{2}ωt = 1
 y^{2}/A^{2} + v^{2}/A^{2}ω^{2} = 1
multiplying through by A^{2}ω^{2}
 y^{2}ω^{2} + v^{2} = A^{2}ω^{2}
now rearrange for v^{2}
 v^{2} = A^{2}ω^{2}  y^{2}ω^{2}
^{}take ω^{2} out as a common factor
 v^{2 = }ω^{2}(A^{2}  y^{2})
square root both sides
 v = ±ω√(A^{2}  y^{2})
Considering the circular motion of a charged particle in a magnetic field, derive an expression for the radius of the particle's circular motion.
The force exerted by the magnetic field is considered to be a centripetal force, and so:
qvB = mv^{2}/r
rearranging this obtains
r = mv/qB
In the early 1900's, experimental evidence suggested that certain phenomena could not be explained using classical physics theory.
State one experimental observation that cannot be explained by classical physics.
 Bohr model of the atom and energy levels for electrons.
 Emission and absorption spectra produced by elements in gaseous form.
 The photoelectric effect
 Black body radiation curves/ultraviolet catastrophe
Describe the effects of damping in simple harmonic motion. Consider:
 Underdamping
 Overdamping
 Critical damping

The effects of underdamping are quite small and result in a slow reduction in amplitude.

The damping is so great that no complete oscillations are seen. (sometimes called heavy damping)

This means that the oscillator comes to rest in the minimum possible time
The effects of underdamping are quite small and result in a slow reduction in amplitude.
The damping is so great that no complete oscillations are seen. (sometimes called heavy damping)
This means that the oscillator comes to rest in the minimum possible time
There exists some well known experimental evidence for waveparticle duality.
Can you name some experimental evidence which shows the
 Particle nature of waves
 Wave nature of particles.
 The photoelectric effect
 Electron diffraction patterns.
Assuming the relationship
y = A cos ωt
derive expressions for velocity and acceleration for an object undergoing simple harmonic motion.
y = A cos ωt
differentiating this gives
v = Aω sin ωt
differentating this again gives
a = Aω^{2} cos ωt
= ω^{2}y
Describe how aurorae are produced in the earth's upper atmosphere
Cosmic rays enter the earth's magnetic field and spiral with helical motion along the field lines until they enter the earth's atmosphere at the north and south poles.
Collisions with atoms in the earth's atmosphere produce energy in the form of light, known as aurora. (Borealis, Northern lights. Australis, Southern lights)
Shown below is an example of a 'black body radiation curve' which shows the irradiance of all wavelengths of radiation emitted by an object.
What is the relationship between the 'peak wavelength' emitted by an object and its temperature in kelvin?
The shorter the 'peak wavelength' of the object, the higher the temperature of the object.
Quantatively, this relationship is known as 'Wein's law' and is given by the relationship
T x λ_{p} = 2.9 x 10^{3}
Simple harmonic motion can be defined mathematically in terms of force and acceleration.
What two relationships can be used to describe simple harmonic motion in the y direction?
F =  ky
and
a = ω^{2} y (where ω = 2πf)
What does the photoelectric effect tell us about the particulate nature of light?
 Photoemission will not happen underneath a 'threshold frequency' of radiation (f_{0}) no matter the irradiance.
 If the light was, as thought classically, one continuous wave, then eventually the electrons would absorb enough energy to escape the material, even at smaller frequencies.
 Each individual photon must have enough energy to release an electron the photon's energy must be quantised.
Quantum Physics describes the behaviour of materials/atoms/molecules at very small (atomic) scales. What is meant by the word 'quantised'?
Properties (such as energy) only exist in well defined states, rather than in a continuous range.
Derive an expression for the kinetic energy of an object underging simple harmonic motion.
Explain, in terms of superposition of waves, how a stationary wave is produced.
Stationary waves are formed by the interference of two waves, of the same frequency and amplitude, travelling in opposite directions.
The displacement of an object undergoing simple harmonic motion can be described by the relationships
y = A sin ωt
and
y = A cos ωt
(depending on initial conditions.)
Sketch a displacement time graph for each of these situations.
What is meant by two waves being coherent?
The two waves have a constant phase relationship (that is the phase difference between any given point on each wave remains constant),
What is the relationship between geometrical path length and optical path length?
Optical path length = n x geometrical path length.
What is the condition for constructive interference in terms of optical path difference?
Constructive interference occurs when
Optical path difference = mλ
What is the condition for destructive interferece in terms of optical path difference?
Constructive interference occurs when
Optical path difference = (m+1/2) λ
How could you calculate the optical path difference if you know the optical path lengths of two coherent waves?
Optical path difference is the difference between the two optical path lengths.
What does it mean if a wave is said to be plane polarised?
If the oscillations of the wave medium are restricted to one dimension only the wave is said to be plane polarised.
A polariser and analyser combination can be used to increase or decrease the transmission of a light wave.
What would be observed if a laser beam was shone through a polariser and then an analyser which were at 90 degrees to each other?
There would be no light transmission through the polariser and analyser combination.
How can the Bohr model of the atom account for line emission spectra?
Electrons orbit the nucleus of an atom in only certain allowed orbits.
Changes between orbits can only produce discrete, fixed quanta of energy, given by ΔE = hf.
This produces discrete frequencies (and wavelengths) of light.
Energy can be measured in either joules or electronvolts.
How do you convert between Joules and electronvolts (eV)?
An electron volt is defined as the energy gained by an electron when accelerated through 1V of potential difference:
W = qV
= 1.6 x 10^{19} x 1
= 1.6 x 10^{19}J
so 1 eV = 1.6 x 10^{19}J
In simple harmonic motion, what is the relationship between angular frequency and the period of oscillation?
ω = 2πf and f = 1/T
so
ω=2π/T.
On a stationary wave, what is meant by the term node?
A point on the stationary wave pattern where there is no disturbance/zero displacement.
On a stationary wave, what is meant by the term antinode?
A point on the stationary wave pattern where there is maximum disturbance/maximum displacement.
What is the condition for constructive interference in terms of phase?
Two waves meet completely in phase crest meets crest.
The phase difference Φ = 0 radians.
What is the condition for destructive interference in terms of phase?
Two waves meet completely out of phase by half a wavelength crest meets trough.
The phase difference Φ = π radians.
The relationship shown below can be used to determine the wavelength of a laser going through a double slit.
Define each of the quantities in the relationship.
Δx = distance between adjacent bright fringes (m)
λ = Wavelength of the laser light (m)
D = distance from double slit to screen (m)
d = distance between slits (m)
The relationship shown below can be used to determine the wavelength of a laser going through a double slit.
What effect would be seen on the interference pattern if a smaller wavelength of light was used?
The distance between adjacent bright fringes, Δx, would be smaller (the fringes would be closer together).
Plane polarised light can be produced by partial reflection from a glass surface as shown below.
The reflected ray will be plane polarised if the angle of incidence is equal to the brewster angle (i_{p}).
What condition must be met to find the brewster angle, and produce plane polarised light?
The angle between the reflected and refracted rays must be 90 degrees as shown below. This will produce a reflected ray which is plane polarised parallel to the surface of the glass.
What is the relationship between the brewster angle and the refractive index of a material?
n = tan i_{p}
Under which condition will a wave undergo a phase change of λ/2 upon reflection?
The wave will be travelling from a medium with a lower refractve index and reflected by a medium with a higher refractive index.
What is the relationship between the optical path difference and the phase difference (Ф) of two coherent waves of wavelength λ?
phase difference Ф (in radians) = (2π/λ) x optical path difference
Interference can be produced by two methods, division of wavefront and division of amplitude.
Give example(s) of an experiment demonstrating
 Interference by division of wavefront
 Interference by division of amplitude
 Young's double slit experiment, experiments using gratings.
 'Bloomed' lenses, thin film interference, 'wedge' fringes, newton's rings.
Shown below is an example of interference by division of amplitude a lens is 'bloomed' with a nonreflective coating.
Derive the expression d = λ/4n where 'd' is the thickness of coating required to give destructive interference.
Optical PD = λ/2 for destructive interference
also from the diagram, Optical PD = 2nd
therefore
2nd = λ/2
d = λ/4n
The phase difference (Φ) between two points on a travelling wave separated by a distance of half a wavelength (x = λ/2) is equal to how many radians?
Φ = x/λ x 2π
so if x = λ/2
Φ = π radians.
The relationship describing a travelling wave is shown below.
y = 4.0 sin2π(8t – 5x)
What is the relationship describing a reflected wave of the same type with half the amplitude, travelling in the opposite direction?
y = 2.0 sin2π(8t + 5x)
Any periodic (repeating) waveform can be created by adding a combination of sine and cosine waves together.
What is the name given to the process of adding waves together?
Superposition of waves
Stationary waves can only be formed by interference at very specific frequencies.
What name is given to these frequencies?
Resonant frequencies.
A stationary wave pattern is shown below.
What is the wavelength of the wave?
The wavelength is 1m.
(There are three halfwavelengths in 1.5m)
An experiment designed to show 'thin wedge' interference is set up as shown below:
What is the relationship used to describe thin wedge interference, and what does each quantity represent?
∆x = distance between bright fringes (m)
λ = wavelength of light (m)
l = length of 'wedge' (m)
d = height of 'wedge' at end (m)
What effect would having a thinner 'wedge' (d) have on the spacing between bright fringes (∆x) in the following experiment?
A thinner wedge would make the spacing further apart.
What is the unit of magnetic induction (magnetic field strength) (B)?
Tesla (T).
What is the unit of phase angle, Φ?
Radians (rad).