Chapter 16
Lecture Three: WaveI (part 2)
HW1
(problems): 16.12, 16.24, 16.27,
16.33, 16.52, 16.59, 17.6, 17.13
Due Friday, Feb. 7.
Superposition of Sinusoidal
Waves
Assume two waves are traveling in the same
direction, with the same frequency,
wavelength and amplitude
The waves differ only in phase
y
1
=
A
sin (
kx

t
)
y
2
=
A
sin (
kx

t
+
)
y
=
y
1
+
y
2
=
2
A
cos (
/2) sin (
kx

t
+
/2)
Sinusoidal Waves with
Constructive Interference
When
= 0, then
cos (
/2) = 1
The amplitude of the
resultant wave is 2
A
The crests of one wave
coincide with the crests
of the other wave
The waves are
everywhere in phase
The waves interfere
constructively
Af_1803.swf
Sinusoidal Waves with
Destructive Interference
When
=
, then
cos (
/2) = 0
Also any odd multiple of
The amplitude of the
resultant wave is 0
Crests of one wave
coincide with troughs of
the other wave
The waves interfere
destructively
Sinusoidal Waves, General
Interference
When
is other than 0
or an even multiple of
, the amplitude of the
resultant is between 0
and 2
A
The wave functions still
add
Use the active figure to
vary the phase
relationship and
observe resultant wave
Sinusoidal Waves, Summary of
Interference
Constructive interference occurs when
= n
where n is an even integer (including 0)
Amplitude of the resultant is 2A
Destructive interference occurs when
= n
where n is an odd integer
Amplitude is 0
General interference occurs when 0 <
< n
Amplitude is 0 < A
resultant
< 2A
16.12: Standing Waves
If two sinusoidal waves of the same amplitude and wavelength travel in
opposite directions along a stretched string, their interference with each
other produces a standing wave.
Standing Wave Example
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 Fall '12
 Vitkalov
 Normal mode, Standing wave, 0.800 m, 0.400 m, 0.180 M