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Chapter 16
Superposition and
Standing Waves
Section 16-1: Superposition of Waves
When two or more waves combine, the resultant wave at any point, is the algebraic sum of the individual waves.
Superposition and the Wave Equation
y3 = c1y1 + c2y2
superposition
Interference of Harmonic Waves
Constructive interference
Destructive Interference
Beats
Phase difference due to a path difference
Waves are in phase
if the phase difference, δ= n(2π)
This results in constructive interference
The waves are exactly out of phase when δ= (n+½)2π
This results in destructive interference
Example 16-2 p 485
Intensity versus path difference for two sources that are in phase.
Two sources that are in phase, or have a constant phase difference are said to be coherent.
The Double Slit Experiment:
doubleslit
Section 16-2: Standing Waves
String fixed at both ends
The standing wave condition is when
L = n(½λ)
and
fn= nν/2L =nf1
A classic Steinway piano
String fixed at one end.
Wave functions for standing waves
String fixed at both ends
wavesuperposition
String fixed at one end
Standing sound waves on the surface of the sun
Some of the many modes of oscillation of a ringing handbell