1. Dr Richard Alexander (G44B)
PA114
Waves and Quanta
Unit 2: Waves
(Problem solving)
Tipler, Chapters 15 & 16
Dr Richard Alexander (G44B)

2. Problem solving lecture
- Wave definitions
- Standing waves and beats
- Wave equation
- Wave energy
- Wave velocity

3. The wave function for a wave on a string is given by:
- In which direction does the wave travel?
- What is the wave speed and wavelength?
- What is the maximum transverse speed
of an element of the string?

4. Show that the superposition of two identical waves
travelling in opposite directions is a standing wave

5. Trig identities:

6. Standing wave

7. Show that the superposition of two waves with
different frequencies results in beats

8. Note heard at mean of the two frequencies,
modulated (beats) at difference between freqs.

9. A wave on a string has mass density m and is
described by the wave function:
Show that this is a solution of the wave equation
(b) By considering the stretching and transverse
velocity of the string, show that energy
propagates along the string at the wave speed.

10. A piano wire is 1 m long, weighs 1 g, and is put under
a tension of 40 N. Find the frequency of the first
3 harmonics of the wire.
What tension would have to be placed on the wire to
make the fundamental middle C (262 Hz)?