Definitions

Question 1

Describe the Doppler effect and how it is theoretically derived

Answer 1

The Doppler effect is the shift in the frequency recorded when there is a relative motion between the observer and wave source.
Classical considers progression of propagating wavefronts relative to the motion of the source and observer
Quantum, waves have quantised energies and momenta, from principles of conservation of energy and momentum

Question 2

What is meant by the terms travelling and standing waves

Answer 2

Travelling waves maintain a constant form that is translated through space as time evolves.
Standing waves maintain a spatially fixed form the is multiplied by an evolving function of time.

Question 3

What is meant by dispersion

Answer 3

Dispersion describes the spreading of a wave packet as it propagates and corresponds to a variation in the phase velocity as a function of the frequency of sinusoidal components. In a dispersive system, the phase and group velocities will differ

Question 4

What is meant by the phase and group velocity?

Answer 4

Phase velocity is the velocity with which a wavefront of given displacement appears to propagate
The group velocity is the velocity with which the overall amplitude of a wave packet appears to propagate

Question 5

What is meant by wave interference

Answer 5

Describes the addition of wave amplitudes or displacements when # or more waves reach the same point at the same time. As amplitude may be positive or negative, the waves interfere either constructively or destructively.

Question 6

Explain what is meant by impedance of a medium in the context of wave motion

Answer 6

Is the measure of resistance to the disturbance by the process driving wave motion.
Related to the ratio of the two properties that are conserved at an interface, and therefore determines the reflectivity at such a boundary. If the impedances are the same on both sides of the interface, the wave is no reflected

Question 7

What is meant by an operator of wave motion

Answer 7

An operator is a mathematical operation that can be applied to a wave function to determine observable properties of the wavefront, such as the frequency, wave number, bandwidth. The observable is found by applying the operator to the wave function

Question 8

What is meant by the Doppler effect

Answer 8

Is the shift is the observed frequency of a wave when there is relative motion between the observer and source

Question 9

Explain the meanings of transverse and longitudinal wave motions, and give and example of each and one that is neither

Answer 9

Transverse waves involve the propagation or medium displacement, or a field component in a direction perpendicular to the direction of wave propagation
Longitudinal waves involve the propagation of a displacement of a field component that is parallel to the direction of propagation.
- Transverse: Electromagnetic radiation
- longitudinal: Thermal Waves
- Neither: Quantum Wavefunctions

Question 10

Explain with examples, the boundary conditions that apply to wave motion

Answer 10

Are the constraints imposed upon a wave at particular position by the presence of external influences
Like the air columns in a clarinet must have at its open end the unperturbed atmospheric pressure.

Question 11

Explain what is a wave

Answer 11

Wave motion is the propagation of a bulk disturbance, where what occurs at one point happens subsequently at each next point

Question 12

What do phasors represent

Answer 12

Represent magnitude (Amplitude) and phase of a wave

Question 13

What is huygens description of wave propagation

Answer 13

Propagation of a wavefront occurs due to the constructive interference of secondary wavelets originating from imaginary sources along the point of the original wavefront. New wavefront formed from the common tangent of each of the imaginary sources

Question 14

What is fermats principle of least time

Answer 14

For a wave travelling between 2 points, the wave will follow the path that takes the least time

Question 15

What is diffraction

Answer 15

Diffraction is the bending or spreading of waves at the encounter an aperture or obstacle.

Question 16

What are continuity conditions

Answer 16

For a wave motion at an interface between two media describe the principles of how the wave behaves when transitioning from one medium to another.
An change in properties of the medium change the wave speed and the partial reflection of the wave

Question 17

What is the convolution theorem

Answer 17

Convolution of 2 wave functions is the product of the Fourier transforms of the 2 wave functions to produce a singular, third wave function

Question 18

What is meant by a Fourier transform? How may it be derived?

Answer 18

The Fourier transform allows a function of time or position to be instead represented as a function of frequency or spatial frequency.
The component with a given frequency is obtained by multiplying the function by a sine wave with the same frequency, and integrating over the range of the function

Question 19

What is meant by Fraunhofer diffraction

Answer 19

Is the modification of a wave by its partial obstruction by an imposed object, mask or aperture

Question 20

What are continuity conditions

Answer 20

For wave motion at an interface between two media describe the principles of how the wave behaves when transitioning from one medium to another