WAVES
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wave = disturbance that propagates
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“disturbance” e.g., displacement of medium element
from its equilibrium position;
propagation can be in medium or in space (disturbance
of a “field”);
mechanical waves:
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when matter is disturbed, energy emanates from the
disturbance, is propagated by interaction between
neighboring particles; this propagation of energy is
called wave motion;
a traveling mechanical wave is a self-sustaining
disturbance of a medium that propagates from one
region to another, carrying energy and momentum.
examples:
 waves on strings,
 surface waves on liquids,
 sound waves in a gas (e.g. in air),
 compression waves in solids and liquids;
it is the disturbance that advances, not the material
medium
transverse wave
displacements perpendicular to direction of
propagation;
longitudinal wave
sustaining medium displaced parallel to direction of
propagation (e.g. sound waves, some seismic waves,
compression waves in a bell);
periodic wave motion
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periodic wave motion:
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particles oscillate back and forth, same cycle of
displacement repeated again and again;
(we only discuss periodic waves)
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terms describing waves:
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crest of the wave = position of maximum
displacement (“highest point of the wave”)
amplitude = amount of maximum displacement
(height of crest above undisturbed position)
wave velocity v = velocity of propagation of wave
crest
wavelength  = distance between successive sameside crests
frequency f = number of same-side crests passing
by a fixed point per second
period T = time for one complete wave oscillation:
period = 1/frequency
unit of frequency: 1 hertz = 1Hz = 1/second
wave velocity (speed of waves) depends on
properties of the carrying medium;
in general: speed of mechanical waves in solids
greater than in liquids, and greater in liquids than in
gases.
relation between speed, wavelength and frequency:
v = f   , i.e. speed = frequency times wavelength
Energy in a wave
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intensity of a wave is a measure of how much power
is transported to a point by the wave;
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intensity = energy flow per unit time, per unit area =
power per unit area,
(where area = area perpendicular to propagation
direction)
energy flow carried by wave: is proportional to the
square of the amplitude and the square of the
frequency;
“inverse square law of wave intensity”:
the intensity of a wave is inversely proportional to
the square of the distance from the source of the
wave
I = P/(4R2)
(source = object emitting the wave)
(I = intensity, P = total power emitted by source,
R = distance from source)
(strictly speaking, only for point-like or spherically symmetric sources,
or if size of the source much smaller than R)
Superposition of waves, interference
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Superposition principle:
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two or more waves moving through the same region
of space will superimpose and produce a welldefined combined effect; the resultant of two or
more waves of the same kind overlapping is the
algebraic sum of the individual contributions at
each point, i.e. the (signed) displacements
(elongations) add.
Huygens' principle
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every point on a wavefront can be considered as a
source, emitting a wave; the superposition of all
these waves results in the observed wave.
consequences: interference, diffraction
interference: superposition of two waves of same
frequency can lead to reinforcement (constructive
interference) or partial or complete cancellation
(destructive interference;
constructive interference: two waves “in phase”,
(i.e. crests of two waves coincide in time) reinforce
each other, resultant amplitude bigger than that of
individual waves;
destructive interference: two waves “completely
out of phase” (i.e. out of phase by 1/2 period, so
that crests of one wave coincide with troughs of
the other)  cancellation; complete cancellation
(extinction) if both waves have same amplitude.
Interference, cont’d
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phase differences can be caused by:
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differences in pathlength; given a pathlength
difference, the phase difference depends on the
wavelength;
travel time difference due to difference in speed in
different media;
reflection;
examples:
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colors of thin films (oil on water, soap bubbles)
dead spots in auditorium
diffraction grating:
 many narrow parallel slits spaced closely
together;
 every slit forms source for wave;
 differences in pathlength from different slits
to some point in space
 phase difference
 wavelength dependent interference
pattern;
 can be used to measure wavelength;
interferometers:
 Michelson - Morley (used to measure “ether
wind”)
 Fabry - Perot
SOUND
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Sound waves propagate in any medium that can
respond elastically and thereby transmit
vibrational energy.
sound waves in gases and liquids are longitudinal
(alternating compression and rarefaction); in
solids, both longitudinal and transversal;
speed of sound is independent of frequency;
speed of sound in air  340m/s at 20o C;
increases with temperature;
 1500m/s in water;
three frequency ranges of sound waves:
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below 20 Hz: infrasonic
20 Hz to 20 kHz: audible, i.e. sound proper
above 20 kHz: ultrasonic, “ultrasound”
pitch is given by frequency e.g. “standard a”
corresponds to 440 Hz
intervals between tones given by ratio of
frequencies (e.g. doubling of frequency - one
octave)
male voice range 80 Hz to 240 Hz for speech, up
to 700 Hz for song;
female voice range 140 Hz to 500 Hz for speech,
up to 1100 Hz for song.