In a material medium, the resorting force is provided by
intermolecular forces. If a molecule is disturbed, the
restoring forces exerted by its neighbors tend to return the
molecule to its original position, and it begins to oscillate. In
so doing, it affects adjacent molecules, which are in turn
set into oscillation. This is propagation of wave.
Bonds can be represented by springs
The spring force is restoring force.
medium – the substance or object in which the wave is travelling.
A pulse: a single disturbance that travels through a medium
What is a wave? A disturbance that moves through something 
rather vague!
Why are waves important?
 waves carry energy 
sometimes a lot
and sometimes even more
the energy from the sun comes to us along
electromagnetic waves– light waves
Travelling/Continuous/Progressive wave:
•
•
•
•
continuous distrurbance
transfer energy from one place to another.
without a net motion of the medium through which they travel.
they all involve oscillations – SHM, of one sort or another.
The important thing is that when a wave travels in a medium,
parts of the medium do not end up at different places.
The energy of the source of the wave is carried
to different parts of the medium by the wave.
Depending on the direction of oscilations of the
medium relative to the direction of propagation
of the wave (energy flow), there are three basic
categories and many more combinations:
Not everything that we call a
wave is a wave actually: If it
results with matter pining up it is
not a wave in physics sense.
Transverse wave
• The particles of the medium oscillate perpendicular to the
direction of energy transfer/propagation of the wave.
• Earthquake secondary waves, waves on a stringed
musical instrument, waves on the rope,
• EM waves: light, radio waves, microwaves…
Longitudinal/Compression wave
• The particles of the medium oscillate parallel to the
direction of energy transfer/propagation of the wave.
• Sound waves in any medium, shock waves in an
earthquake, compression wave along a spring…
direction
of energy
transfer
oscillations of air molecules are in the
same direction as energy transfer
rarefaction – region in a medium with low pressure, low density.
compression – region in a medium with high pressure, high density.
Relationship between pressure (longitudinal)
and transverse graphs
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about sound
•
the diaphragm of the speaker
moves in and out
•
the air molecules jiggle back and
forth in the same direction as the
wave/ energy transfer
•
the same as the change of density in
the case of shock eartquake wave
Transverse wave graph looks very similar to the actual wave.
For a longitudinal wave the graph is not so easy to see.
There are two types of waves regarding medium.
1. Mechanical waves
They need medium to propagate, where paricles of the medium
oscillate as the wave passes through.
• a disturbance that propagates through a medium –
solids, liquids or gases thus transferring energy
from one place to another.
•
waves on strings
•
•
waves in water – ocean waves
sound waves – pressure waves in gas,
solid or liquid
• in short, every wave that is NOT EM wave
• As the disturbance moves, the parts of the
material (segment of string, air molecules)
execute harmonic motion (move up and
down or back and forth)
Disturbance travels not the medium
• a disturbance that propagates through a medium –
solids, liquids or gases thus transferring energy
from one place to another.
•
•
waves on strings
waves in water
– ocean waves
• sound waves – pressure waves in air, solid
or liquid
• in short, every wave that is NOT EM wave
• As the disturbance moves, the parts of the
material (segment of string, air molecules)
execute harmonic motion (move up and
down or back and forth)
2. Electromagnetic waves
The other ones, ELECTROMAGNETIC WAVES, do not need
medium to propagate. They come to us from faraway stars
traveling through a vacuum. Of course, they can travel through
a medium, but when they travel through medium, they do
definitely not make particles of the medium vibrate at EM
frequency. Just imagine window oscillating at frequency of
visible light, ~ 1015 Hz. On the other hand when a sound wave
(mechanical wave) travels through a window it will make glass
vibrate at that frequency.
Electromagnetic Waves
A wave of energy. The electric
and magnetic field oscillate
(change magnitude and direction)
1. EM emission occurs when electron fall from an
excited state to a state of lower energy. Energy of EM
wave equals the electron’s change in energy.
_
_
+
before photon emission
+
~ 10-8 s later – photon emission
EM waves are produced by accelerated charges
antenna
2. a charged particle oscillating
about an equilibrium position
is an accelerating charged particle.
3. PLASMA - highly ionized gas (a fourth state of matter)
- the atoms are nearly all fully ionized and the substance consists of
electrons and atomic nuclei (or positive ions)
- "bremsstrahlung“: the electrons are accelerated, and the gas cloud
emits radiation continuously.
Some sources of free-free emission
include ionized gas near
star-forming regions or
Active Galactic Nuclei (AGN).
How fast does it go?
•
The speed of the wave is the speed of energy transfer and is not
the same as the speed of the particle of the medium oscillating
around equilibrium position.
The wave speed is determined by:
● the stiffness of the material
 more stiff  higher speed
each segment of medium is in tighter contact with its neighbor
●
density - more difficult to change the velocity of larger masses
than smaller ones
 greater density more inertia  lower speed
How fast is transverse wave in strings?
The wave speed in strings is determined by:
● the tension in the string
more tension  higher speed
the mass per unit length of the string (whether it’s a heavy rope
or a light rope)
T
 thicker rope  lower speed
v
●
m/ L
Why do waves travel faster in steel than in air?
● As far as waves are concerned, the difference between
steel and air is that steel is stiffer and denser than air.
● But the stiffness of steel is much greater than that of air,
even though the density of steel is greater.
● Consequently, the stiffness factor influences the wave
speed more and waves travel much faster in steel than in
air.
Speed of sound in:
air: 343 m/s
water: 1500 m/s
steel rod: 5000 m/s
helium: 1005 m/s
bone: 3000 m/s
glass: 4500 m/s
Waves in a violin string:
A-string: 288 m/s, G-string: 128 m/s
Transverse waves cannot propagate in a gas or a
liquid because there is no mechanism for driving
motion perpendicular to the propagation of the wave.
The speed of transverse waves in solids are about
0.6 times the speed of longitudinal waves in solids.
The earth is shaking
Earthquakes produce both
longitudinal waves
(called “P” waves – primary - faster
– the first to be detected by seismologists)
and
transverse waves
(called “S” waves – secondary - slower
– the second to be detected by seismologists)
more destructive.
earthquakes
Definitions associated with waves
Amplitude, A
● is the maximum displacement of a particle from its equilibrium position.
● It is also equal to the maximum displacement of the source that produces
the wave.
● From SHM, energy of a wave ∞ A2. If the wave doesn’t lose any of its
energy its amplitude is constant.
Period, T
● is the time that it takes a particle to make one complete oscillation.
● is the time taken for one complete wave to pass any given point.
Frequency, f
● is the number of oscillations made by a particle per second.
● 50 Hz means 50 oscillations per second
f=
1
T
T=
1
f
Wavelength, λ
● This is the distance along the medium between two successive particles
that have the same displacement (that are in phase)
(e.g. from crest to crest, or from compression to compression)
Wave speed, v
● The speed at which wavefronts pass a stationary observer.
● It is constant, depending on the medium only.
Intensity, I
● The energy that a wave transports per unit time across unit area of the
medium through which it is travelling is called the intensity.
● Intensity of a wave is the power per unit area that is received
by observer.
● The unit is W/m2.
● Hence for a wave of amplitude A, we have that I ∞ A2
A displacement vs. position graph shows the displacement of all
points along the wave. A snapshot of a wave at one instant of time.
Transverse wave:
displacement vs. x,
Longitudinal wave:
density vs. x or
pressure vs. x
A displacement vs. time graph shows the oscillations of one point on the
wave. All other points will oscillate in a similar manner, but they will not
start their oscillations at exactly the same time.
Transverse wave:
displacement vs. t,
Longitudinal wave:
density vs. t or
pressure vs. t
Wave Equation
Koala measures time between crests to be 0.5 s.
Koala measures distance between crests to be 1m.
clever koala finds the speed of the wave to be: v = 2 m/s
wave speed =
v=
distance
wavelength
=
= wavelength  frequency
time
period
λ
= λf
T
This applies to all waves  water waves, waves on
strings, sound waves, radio, light . .
Waves with different frequncies and wavelength will have the same
speed in one medium, determined by that medium. If you shake the
string faster (greater freq.) the wavelength will be smaller and vice versa
A sound wave produced by a clock chime is
heard 515 m away 1.5 s later.
(a) What is the speed of sound in the air there?
(b) The sound wave has a frequency of 436 Hz.
What is the period of the wave?
(c) What is the wave's wavelength?
(a) v = d/t = 515/1.5 = 343 m/s
(b) f = 1/T = 1/436 = 2.29x10-3 s
(c) v =  f →  = v / f = 0.87 m
A hiker shouts toward a vertical cliff 465 m away. The echo is heard
2.75 s later. (a) What is the speed of sound in air there? (b) The
wavelength of the sound is 0.75 m. What is the frequency of the
wave? (c) What is its period?
(a) v = distance/time = 2d/t = 2·465/2.75 = 338 m/s
(b) v =  f → f = v/ = 338/0.75 = 451 Hz
(c) T = 1/f = 2.22x10-3 s
If you wanted to increase the wavelength of waves in a rope
should you shake it at a higher or lower frequency?
v=f
v depends only on the medium. Therefore for given
medium it is constant. So if wavelength increases the
frequency decreases. You should shake it at lower
frequencies. CHECK IT, PLEASE
A stone is thrown onto a still water surface and creates a wave.
A small floating cork 1.0 m away from the impact point has the
following displacement—time graph (time is measured from the
instant the stone hits the water):
Find (a) amplitude
(b) the speed of the wave (c) the freq.
(a) A = 2 cm
(b) v = d/t = 1/1.5 = 0.67 m/s
(c) f = 1/T = 1/0.3 = 3.33 Hz
(d) λ = v/f = 0.666/3.333 = 0.2 m
(d) wavelength
Wavefronts propagating from a point source
Ray - direction of wave
direction of energy transfer
wavefront is the locus of points having the
same phase. Set of points with the same
displacement from equilibrium position and
the same velocity vector.
plane waves: far away from the
source circular wavefronts
become straight lines
EM waves striking the
earth are plane waves
Electromagnetic waves – Electromagnetic spectrum
● Visible light is one part of a much larger spectrum of similar
waves that are all electromagnetic.
● EM waves are produced/generated by accelerated charges.
● EM wave is made up of changing electric and magnetic fields.
● The electric and magnetic field components of EM wave are
perpendicular to each other and also perpendicular to the
direction of wave propagation – hence EM waves are
transverse waves.
● They all travel travel through vacuum with the same speed –
speed of light c:
c = 2.99 792 458 x 108 m / s
c ≈ 3 x 108 m/s
● This speed is completely independent of the frequency or the
wavelength of the wave!!
● EM waves are waves, so: c = λf
● greater λ smaller f
● This is a large speed ≈ 186,000 mi/s. If the beam of
light could curve it would travel around the world
about seven times in a single second.
● On the other hand, when one recalls that the nearest
major galaxy to our own, the Andromeda galaxy, is
about 2.9 million light years away, meaning that it
takes 2.9 milion years for the light to reach the earth,
the speed of light doesn’t appear so great after all.
● The energy of a wave is directly proportional to its
frequency, but inversely proportional to its wavelength.
In other words, the greater the energy, the larger the
frequency and the shorter (smaller) the wavelength.
Short wavelengths are more energetic than long
wavelengths.
● Although all EM waves are identical in their nature,
they have very different properties, due to different
wavelengths and frequencies, and therefore energy
that they carry along.
Electromagnetic waves – Electromagnetic spectrum
What is the origin of sound?
Vibrations of objects - a string, a reed, vocal cords, earthquake
How does sound travel in air?
• The vibration of the fork causes the
air near it to vibrate
• Longitudinal wave – air molecules vibrate
to and fro along direction of wave
• Analogy with opening and shutting a door periodically:
Open door inward: a compression travels across room (via
molecules pushing neighbors)
Close door: a rarefaction travels across room – some molecs
are pushed out of room so leave lower pressure behind.
Swing door open and shut periodically – get periodic
compression-rarefaction wave across the room.
• Tuning fork – is exactly this action on a smaller, faster scale:
prong vibrating is like the door opening and shutting.
• Radio loudspeaker – cone that vibrates in synch with
electric signal, causing neighboring air molecules to
vibrate …eventually sound wave filling the room
The pressure waves make
your eardrum vibrate
frequency of sound waves = pitch
High pitch – high frequency (a piccolo),
whereas low pitch means low frequency (fog horn)
Frequencies of the Sound
• Human ear can hear between 20 – 20 000 Hz.
• Infrasonic – below 20 Hz
• Ultrasonic – above 20 000 Hz
Dogs can detect freq as low as 50 Hz and as high as
45,000 Hz while
Cats detect freq between 45 Hz and 85,000 Hz.
Bats who rely on reflection of sounds that they emit
for navigation can detect freq as high as 120,000 Hz.
Dolphins can detect freq as high as 200,000 Hz.
Infrasound and sound in a range of 5 Hz to 10,000 Hz
can be detected by elephants.
Speed of sound in air
Speed does not depend on loudness (amplitude),
nor on pitch (freq).
• Speed of the sound depends of course on the medium.
• Air at 20 C: 343 m/s = 767 mph  1/5 mile/sec
• increases with temperature, humidity, right wind
Low and high freq have the same speed.
Higher freq waves have smaller wavelength, and
lower freq waves have longer wavelengths since
product λf = v is same.
Autofocusing cameras emit a pulse of very high frequency
(ultrasonic) sound that travels to the object being
photographed, and include a sensor that detect the
returning reflected sound. Calculate the travel time of the
pulse for an object (a) 1.0 m away (b) 20 m away.
Temperature is 200.
v = 343 m/s
a) d = 2 m
t = d/v
d = vt,
t = 0.006 s = 6 ms
b) d = 40 m
t = d/v
d = vt,
t = 0.15 s = 150 ms
• speed of light is a million times as great
The light from a lightning flash reaches us almost
instantaneously; the corresponding sound wave, generated
by heated expanding air near the lightning bolt, travels
toward us at about 340 m/s.
•we see lightning before we hear thunder
• we see a distant tree fall to the ground before we
hear the thud…
v  1/3 km/s → 3 seconds rule: 3 s delay in the arrival of thunder after
lightening correspond to a distance of 1 km
v  1/5 mi/s → 5 seconds rule : 5 s delay for every mile.
Sound travels in other media too
• Through anything that is elastic i.e able to change
shape in response to an applied force and then
resume its original shape once force is removed.
• putty is not elastic but steel is
• Sound pressure waves in a solid, liquid or gas
Sound generally travels fastest in solids, then in liquids,
and slowest in gases
air at 20 C: 343 m/s, 4x as fast in water, 15x as fast in steel
Also, generally less dissipation (ie fading away) in
solids and liquids than in air,
• Can hear a distant train coming more clearly and
sooner if put ear against the rail
• Motors of boats –or fingernails clicking - sound much
louder to someone under water, than to someone above.
Sound needs a medium – won’t travel in a
vacuum since nothing to compress and expand
Some people claim they have an extra-sensory perception, citing the
fact that they awaken from a deep sleep for no reason, get out of bed
and walk to the window just in time to hear explosions from a distant
munitions plant.
Premonition ??
Actually this can be explained by comparing the speed of sound
through earth and through air! Assume the tremor of the sound wave
traveling through earth awoke the person, who then walked to the
window just in time to hear the sound wave traveling through the air.
That’s why dogs sleep on their ears.
Sound travels through rock at 3000 m/s, and through
air at 340 m/s. If the munitions plant is 1 km away,
calculate the time interval between the tremor waking
the person and him hearing it through the air.
d = vt ,
so
t = d/v
So time through rock = (1000m)/(3000 m/s) = 0.33 s
Time through air = (1000 m)/(340 m/s) = 2.94 s
So time interval = 2.94 -0.33 = 2.6 s
Infrasonic sound f < 20 Hz
Sources of infrasonic waves include earthquakes, thunder,
volcanoes, and waves produced by vibrating heavy machinery. This
last source can be particularly troublesome to workers, for infrasonic
waves – even though inaudible – can cause damage to the human
body. These low freq waves act in a resonant fashion, causing
considerable motion and irritation of internal organs of the body.
Infrasound is used in the nature for communication:
elephants (~ 15Hz) couple of kilometers,
whales – as sound travels faster in water (v ~ 1500 m/s) than in air,
the call can be heard over distances of thousands kilometers.
Ultrasonic sound f > 20 kHz
Ultrasound is used for echolocation: dolphins, bats, sonar, sonograms
Sonar appeared in the animal kingdom long before it was developed by
human engineers.
So when ultrasound is emitted toward obstacle it will be
reflected back and detected.
dolphins,
ocras,
whales
To echolocate an object one must have both emitter and detector.
If the wavelength of an emitted wave is smaller than the obstacle
which it encounters, the wave is not able to diffract around the
obstacle, instead the wave reflects off the obstacle. Reflected wave
is caught by detector giving it information on how far (2d = vt) and
how big is the object (reflection from different directions)
The ultrasound bats typically chirp is ~ 50 000 Hz.
What is wavelength of that sound?
The speed of sound wave in air is ~ 340 m/s.
v = f so  = v/f
 = 0.0068 m = 0.7 cm
So, bats use ultrasonic waves with  smaller than the dimensions of
their prey (moth – couple of centimeters).
SONAR (sound navigation ranging):
Ships use SONAR to determine the depth of water they are in.
The transmitter emits pulse,
receiver detects reflected pulse.
By timing how long the echo takes to come back and knowing the
speed of sound in water, the depth can be calculated
Why do I sound funny when
I breath helium?
• Sound travels twice as fast in helium, because
helium is lighter than air
• Remember the golden rule v =   
• The wavelength of the sound waves you make with
your voice is fixed by the size of your mouth and
throat cavity.
• Since  is fixed and v is higher in He, the
frequencies of your sounds is twice as high in
helium!
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