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