PHYS/MUS 102 , SPRING 2015

Wave Interference

Longitudinal drawn as Transverse Waves

1. It’s a longitudinal wave

2. But it can be represented by drawing our typical sine wave

What happens when 2 pulses interfere?

Constructive Interference Destructive Interference

Wave interference (aka superposition)

What happens when 2 sources with different frequencies interfere?

Answer: Beats!

fsum =

Questions: Where does occur in a music context, and what will this sound like?

Tune up

Two-source interference

Quantifying intensity maxima

m = 0

m = 1

m = 2

m = -1

m = -2

d

L

z

Source 1

Source 2

Phase shift

0 2 4 6 8 10 12 14 16 18 20-1.5

-1

-0.5

0

0.5

1

1.5

x (m)

Source 1

Am

plitu

de (

arb.

uni

ts)

0 2 4 6 8 10 12 14 16 18 20-1.5

-1

-0.5

0

0.5

1

1.5

x (m)

Source 2

Am

plitu

de (

arb.

uni

ts)

f

Predicted (theoretical) locations of maxima/minima

Maxima occur where:

ml = d sin q = d (z/L) m = …-2, -1, 0, 1, 2

Minima occur where:

(m+1/2)l = d sin q = d (z/L)

Symphony of Superposition

Image sources

Boston University http://sirius.ucsc.edu/demoweb/cgi-bin/?waves-visible-intermodel http://www.paulfriedlander.com/text/timetravel/experiment.htm http://web.sbu.edu/chemistry/wier/electrons/young.html http://hyperphysics.phy-astr.gsu.edu/hbase/sound/beat.html#c2 http://www.animations.physics.unsw.edu.au/waves-sound/interference/ http://www.animations.physics.unsw.edu.au/jw/beats.htm http://www.phys.unsw.edu.au/jw/uncertainty.html