Classical And Quantum Waves And Oscillating Systems

Question 1

What are nodes and anti-nodes

Answer 1

Nodes are points of zero transverse motion

Anti-nodes are where you get maximum transverse displacement

Question 2

How does a Fourier series be used to express and arbitrary vibration of a string of fixed lengthen as a superposition of normal modes.

Answer 2

A Fourier series takes a complex vibration and breaks it into a sim of simple, natural vibration modes that fit the boundary conditions of the string

Question 3

What is the super position of a wave?

Answer 3

The superposition of a wave refers to the combination of two or more waves overlapping in the same pace at the same time to create either constructive or destructive interference.

Question 4

How do noises cancelling headphones use superposition to reduce ambient noise?

Answer 4

Destructive interference is used to create noise cancellation. This is achieved when by listening to the ambient noise and feeding back a signal to the speakers in anti-phase to the ambient noise.

Question 5

What is the beat period

Answer 5

Half the modulation period

(T = pi/omega_mod)

Question 6

In a wave of form y=2Acos(w1t)cos(w2t) what is the modulation angular frequency and what is the fast oscillation frequency?

Answer 6

w1 = fast oscillation angular frequency

w2 = modulation angular frequency

Question 7

In Newtons 2nd law :

m(d^2x/dt^2) = -kx - b(dx/dt) + F_0cos(wt)

Explain all forces

Answer 7

First term comes from Newton’s 2nd Law

Second term is the spring restoring force if the pendulum

Third term is the velocity dependent damping force (b is a resistive coefficient (drag of friction))

The fourth term is the driving force

Question 8

Describe the Photoelectric effect

Answer 8

The photoelectric effect shows that light is quantised and that we can therefore interpret it in terms of particles.

Question 9

What does a wave packet represent

Answer 9

The probability of finding the particle in a particular state

Question 10

How can a particle be described in terms of matter waves ?

Answer 10

A particle can be described in terms of matterwaves as a wave packet which consists of a superposition of a large number of waves with wave numbers in a range of delta k around k where k is the central wave-number of the wave packet

Question 11

What is the physical meaning behind the parameter gamma

Answer 11

In a damped system gamma = b/2m and is the damping coefficient