Waves are closely related to oscillations

1
Chapter 18 Superposition and Standing Waves
Reading assignment Chapter 18.5-18.8 Homework
(due Wednesday, Nov. 16, 2006) Problems Q3,
Q12, 7, 8, 13, 31, 34, 35, 47

• Waves are closely related to oscillations
• Well mainly deal with sinusoidal waves.
• - Water waves Water molecules oscillate in a
  circle
• - Sound waves Air molecules oscillate back and
  forth
• - Stadium waves People move up and down
• - Electromagnetic wave (in Physics 114)

2
Superposition and interference

• If two traveling waves are moving through a
  medium, the resultant wave function is the
  algebraic sum of the wave functions of the
  individual waves.
• Two traveling waves can pass through each other
• When waves meet we can get constructive or
  destructive interference

Constructive interference
Destructive interference
3
Black board example 17.3 Constructive interference
Two pulses are traveling toward each other at 10
cm/s on a long string as shown. Sketch the shape
of the string at time t 0.6 s.
4
Superposition principle
If two (or more) waves move in the same linear
medium, the net resulting wave is equal to the
algebraic sum of the two (or more) individual
waves.
5
Superposition of two sinusoidal waves with the
same wavevector, k, and angular frequency, w. One
wave is shifted with respect to the other by a
phase constant F.
Resultant wave
6
Resultant wave
Constructive interference (Amplitude of resultant
wave is 2A) (The waves are in phase) cos (F/2)
1 Thus F 0, 2p, 4p, 6p,
Wave 1 and 2
Resultant wave
7
Resultant wave
Destructive interference (Amplitude of resultant
wave is 0) (The waves are out of phase) cos
(F/2) 0 Thus F p, 3p, 5p,
Wave 1
Wave 2
Resultant wave
8
Resultant wave
Interference with a random phase constant
F Waves just add up
Wave 1
Wave 2
Resultant wave
9
Reflection of a traveling wave on rigid wall
- If a wave encounters a denser, new medium,
or a rigid wall, it gets reflected. - In this
case the reflected pulse is inverted upon
reflection
10
Reflection of a traveling wave on a loose end
- If a wave encounters a less dense medium or
an end it also gets reflected. - In this case
the reflected pulse is not inverted upon
reflection.
11
Transmission Light string ? heavier string
The transmitted pulse is not inverted. The
reflected pulse is inverted.
12
Transmission Heavy string ? light sting
The transmitted pulse is not inverted. The
reflected pulse is not inverted.