PHY1106 On Line Resources
Dr Pete Vukusic
The following online resources support the parts of PHY1106, Waves and Oscillators
delivered by Dr Vukusic.
Module description
Reduced lecture notes
These comprise some diagrams and text of the lecture notes but are not
complete: i.e. they will not be a substitute for attendance at lectures!.
Lecture 1.
Introduction; setting the scene for undamped SHM; equation of motion;
solution to equation of motion.
Lecture 2.
Phase angle; phase relation between d, v and a;
energy of SHM [PE derivation].
Lecture 3.
SHM energy [KE and total E]; summary so far; introduction to complex numbers;
complex numbers in SHM.
Lecture 4.
Damped SHM introduction; damped equation of motion and solution; three
categories of damped motion.
Lecture 5.
Logarithmic decrement; energy dissipation in damped SHM; intro to the forces
damped oscillator.
Lecture 6.
Implication of "j" on phase; mechanical impedance, forced oscillation
analysis [full derivation].
Lecture 7.
Behaviour of displacement vs. frequency [resonance and phases]; behaviour of
velocity vs. frequency; velocity resonance; average power[ full derivation].
Lecture 8.
Power resonance curve; Q-value for resonance; intro to electrical A.C.
Lecture 9.
Basic ideas re. R, C and L. Complex notation and V-I relations for R, C and
L components in a circuit and phasor diagram representation.
Lecture 10.
Combining R, C and L in a series circuit. complex expression for series LCR
impedance. Meaning of reactance. Phasor representation. Mention of parallel
circuits.
Lecture 11.
RMS expression for V and I. Power, resonance and Q-value for in AC circuits.
Practice questions.
Lecture 12.
Basic wave definitions and concepts; mathematical forms; wave direction; phase
velocity and particle velocity.
Lecture 13.
The wave equation (partial differential form); general solution to the wave
equation; wave on a stretched string example; velocity of wave on a string.
Lecture 14.
Energy transfer and energy density for waves on a string; rate of energy
propagation down a string; introduction to superposition of waves
Lecture 15.
Superposition of waves generally; mathematical form of adding two waves with the
same k; nodes and antinodes in a standing wave; energy transfer in a
standing wave; normal modes in a stretched string.
Lecture 16.
Partial standing waves formed by superposition of waves with similar frequency
and k; occurrence of wavepackets due to superposition; description and formula
for group velocity and its contrast to phase velocity.
Lecture
17.
Dispersion of waves; occurrence of normal dispersion and anomalous dispersion;
the wave velocity (i.e. phase velocity and group velocity) conditions which
determine what form of dispersion prevails in a systems; dependence of
anomalous dispersion on damping.
Lecture
18.
Introduction to the concept of characteristic impedance of a medium and its
associated equations; transmission and reflection of waves from boundaries (as a
result of impedance mismatch between neighbouring regions on either side of
boundary; e.g. waves incident on the junction between two strings; deriving
equations for R and T in terms of impedance z.
Lecture 19.
Derivation
of expressions for transmitted and reflected power at a junction between
two media of different impedance z;
consideration of energy
conservation in the special cases discussed in lecture 18; understanding
of the concept of impedance matching at an interface in significant detail;
derivation and manipulation of reflection and transmission coefficients (in
terms of z), for the case of a
quarter-wave transformer (impedance matching case), so that zero reflection is
produced.
Lecture 20.
Examination of the physics of waves propagating in periodic structures (such as crystals);
developing the equation of motion for waves on a stretched string of equally
spaced beads; solving this equation of motion and subsequent derivation of the
dispersion relation for waves on the system; discussion of the properties of
this dispersion, with particular reference to the first Brillouin zone.
Lecture 21.
Examining the motion
of atoms at special points on dispersion curve; significance of the first
Brillouin zone (all possible modes of vibration are described); showing
that modes outside the first Brillouin zone turn out to be equivalent to ones inside
(but contain redundant information); deriving
the wave equation for another type of wave
i.e. longitudinal
(sound) waves in a solid bar and to
derive expressions for its phase velocity.
Lecture 22.
Longitudinal waves in a solid bar, phase velocity and impedance derivation;
longitudinal waves in a gas deriving then solving the wave equation to produce
the phase velocity and impedance of the gas in terms of Cp, Cv and the bulk
modulus B, etc.
Problems sheets and lecture objectives
These should be used as a follow-up to lectures, and may also be
discussed with your tutors. If you have any difficulties with them or
with the lecture content and key ideas, please contact me (P.Vukusic@ex.ac.uk).
Short answers to exam papers:
Links to useful web resources:
See also: Physics resources
by other people.
