The Interference of
Sound Waves
The Principle of Superposition
The Principle of Superposition states that when 2
waves interfere, the resulting displacement of
the medium at any location is the algebraic sum
of the displacements of the individual waves at
that same location. Example:
The Principle of Superposition
Each pulse has a constant speed of 1 cm/s.
When t=2sec, what is the height of the
resultant pulse at (a) x=3cm and (b) x=4cm?
Constructive Interference
The sum of two crests is referred to as a supercrest.
The sum of two troughs is referred to as a supertrough.
Destructive Interference
Complete destructive interference results in nodes.
Demo
The Effect of Interference
An increase in
amplitude
indicates an
increase in energy,
which for sound
waves means an
increase in the
intensity or volume
of the sound.
2-Source Interference
Two sources (here,
two speakers) will
produce an
interference pattern.
2-Source Interference
Two sources (here, two
speakers) will produce
an interference pattern.
Areas of constructive
interference will
experience an increase
in volume.
2-Source Interference
Areas of destructive
interference (the grey
lines, called nodal lines)
will experience a
decrease in volume.
2-Source Interference
When 2 waves always meet
condensation to
condensation and
rarefaction-to-rarefaction,
they are said to be exactly
in phase.
When 2 waves always meet
condensation-torarefaction, they are said to
be exactly out of phase.
2-Source Interference
Auditoriums and many other
public spaces are designed
with walls (and ceilings and
baffles) that will trap and
absorb sound energy rather
than reflect it so the
reflections cannot interfere
with the original waves and
distort the sound.
2-Source Interference
For 2 wave sources vibrating in phase:
Constructive interference occurs when the
difference in path lengths is 0 or an integer
number of wavelengths.
2-Source Interference
For 2 wave sources vibrating in phase:
Destructive interference occurs when the
difference in path lengths is a half integer number
of wavelengths.
Noise-Reduction Headphones
Noise-reduction
headphones cancel
ambient sound by
producing sound that
is ½ wavelength out
of phase with the
ambient sound (this
works best for single
frequencies).
Example
Two in-phase loudspeakers are
separated by 3.2m. A listener
is situated at point C, which
is 2.4m in front of speaker B.
Both speakers are playing
identical 214-Hz tones, and
the speed of sound is 343
m/s. Does the listener hear
a loud sound or no sound?