Waves and Sound
I. Wave Characteristics
A.  Definition
A wave is a transfer of ENERGY from one point to another without the
transfer of material between the points
WAVES “MOVE” ENERGY, NOT MATTER
Amplitude: the height of the wave, measured in meters.
Wavelength (λ): the distance between adjacent crests, measured in meters.
Period: the time it takes for one complete wave to pass a given point, measured in
seconds.
Frequency: the number of complete waves that pass a point in one second, measured
in inverse seconds, or Hertz (Hz).
Speed: the horizontal speed of a point on a wave as it propagates, measured in meters /
second.
crest
trough
1
B. Some basic equations relating wave properties
1
υ=
T
1
T=
f
v = λυ
frequency (Greek letter ν)
period
speed
Be careful interpreting this equation. It would seem
that changing wavelength would change wave speed
but it does not.
This has to do with how wavelength and frequency are
related. Doubling the wavelength does not double
the speed because it has the effect of reducing the
the frequency by half. SPEED REMAINS THE SAME.
WAVE SPEED DEPENDS ON THE MEDIA IN WHICH THE WAVE TRAVELS.
2
II. TYPES
A. MECHANICAL WAVES-move through a media (solid, liquid, or gas)
longitudinal-medium displacement is in the same direction the wave propagates
transverse- medium displacement is perpendicular to the direction the wave propagates
Water wave are capable of combining both types of motion. Therefore, an object
suspended in the wave moves in a circle as the wave propagates.
Animations of these motions can be found here:
wave motion animations
B. STANDING WAVES-waves whose movement is constrained to a constant position.
Plucking the string of an instrument creates a standing wave. See sounds lesson.
Holding a rope at both ends and shaking it creates standing waves.
The point(s) on a standing wave that remain stationary are called nodes.
The point(s) of highest amplitude are called antinodes, found halfway between nodes.
3
C. ELECTROMAGNETIC WAVES-transverse waves that DO NOT require a medium
through which to travel.
They have an electric field and a magnetic field that propagate in the same
direction but the fields are perpendicular to each other.
They can be POLARIZED. This means they can be filtered so that only
one direction of the electric field passes a polarizing filter.
4
III. Adding Waves-Interference
The nodes and antinodes of waves that are IN-PHASE “line up”
When added, a wave with a larger amplitude results
The nodes and antinodes of waves that are out of PHASE are “off set”
When added, they cancel
5
IV. REFLECTION, REFRACTION, and DIFFRACTION (boundary behaviors)
Very basic information here. We will study these later in OPTICS.
REFLECTION: The reflected waves
bounces off the surface at the same
angle that the incident waves strikes
the surface.
DIFFRACTION occurs when waves
change direction (bend) around
an object or pass through and
opening in a barrier.
REFRACTED waves change direction (bend) when they
enter a new medium. This causes a change in the
velocity and wavelength of the waves.
6
V. SOUND
A. Overview
SOUND is produced only when a media is present to transmit the waves.
The more ELASTIC the media, the FASTER the sound wave travels.
Sound is caused by the vibration of matter.
The medium (air generally) transmits the vibrations by longitudinal waves.
The faster (more frequent) the vibrations the higher the pitch.
Very low frequency sounds are called infrasonic.
Very high frequency sounds are called ultrasonic.
SOUND WILL NOT TRAVEL IN A VACUUM.
B. How it travels
Sound waves are MECHANICAL waves. Sound waves are PRESSURE waves.
They cause the particles of the carrying medium (air) to compress.
A region of compressed air leaves a region of space with fewer air particles-rarefied
air. Particles rush into the rarefied space. A vibrating object causes these
pulses of compressed and rarefied air (waves) to travel in all directions.
When the pulses reach you ear, you interpret the sound.
7
dark regions are
compressed air.
increasing frequency
“thin” regions are
rarefied air.
The distance between
compressed regions
are the wavelength of the
sound wave.
The number of them hitting your
ear per given time is the frequency.
The more of them per given time,
the higher the pitch
tuning forks vibrating with different frequencies.
8
C. Sonic Boom
When a boat outruns the waves it produces in water, a bow wave is produced.
The shape is a V pattern when the wave
crests overlap each other.
Shock wave in air is similar
The SONIC BOOM is created when a moving object is moving faster than
the sound waves it produces. The overlapping wave crests reach your ears
at the same time and are perceived as a loud cracking noise.
sound travels in air at about 1 atm at a rate of 343 m/s
9
D. Doppler effect
The Doppler effect applies to electromagnetic radiation (light) as well as sound waves.
The Doppler effect is observed for MOVING objects emitting light or sound waves.
How you perceive the effect depends upon your location relative to the wave source.
SOUND
sound source moving away
from observer. Low pitch.
sound source moving toward
observer. High pitch.
LIGHT
light source moving away
from observer. Shift to
longer frequency…RED
SHIFT
light source moving toward
observer. Shift to shorter
frequency…BLUE SHIFT
10
VI. SOME PROPERTIES OF SOUND
A. LOUDNESS
The energy of a sound wave is proportional to the amplitude of the wave. The higher
the amplitude, the more energy it carries:
E ∝ A2
E is energy
A is amplitude
11
LOUDNESS, continued
As sound moves away from the object producing it, the INTENSITY decreases. The
intensity of the sound wave (roughly how loud it sounds), is inversely proportional to the
square of the distance away from the source. INTENSITY describes HOW MUCH
ENERGY is transported per a given time.
Intensity =
P=
E
tr 2
E
t
P
Intensity = 2
r
E is energy
d is distance from source, r2 is Area
P is power
This diagram is a 3D
drawing of what waves do
as they move further from
the source.
INTENSITY (LOUDNESS) decreases
RAPIDLY with DISTANCE
12
LOUDNESS, CONTINUED
LOUDNESS, or intensity, is reported using the DECIBEL scale.
The decibel scale is a LOG scale (remember pH?). The decibel scale is based
on a value called the THRESHOLD OF HEARING (TOH).
This is the lowest intensity sound that most people can hear.
TOH = 1 x 10-12 Watts/m2
Sound 10x more intense than TOH has a decibel value of 10
Sound 100x more intense than TOH has a decibel value of 20
Sound 1000x more intense than TOH has a decibel value of 30
I
dB = 10 log
Io
dB is decibels (1 Bel = 10 dB)
I is intensity of the sound
Io is the TOH
13
B. FORCED VIBRATIONS
Forced vibrations occurs when a vibrating object causes another object nearby
to vibrate.
image from Cliffnotes
C. NATURAL FREQUENCY
An object that is struck, thumped, whatever, might begin to vibrate. The
frequencies at which the object vibrates after being struck is the natural frequency
of the object.
Natural frequency is responsible for the characteristic sounds an object makes.
For example, if you closed your eyes and I dropped a pencil or a basketball
on the floor, you’d be able to tell which one based on experience.
Because of their composition and shape, their natural frequencies differ.
14
D. RESONANCE
Resonance occurs when the forced vibration on an object match its natural
frequency.
This causes the AMPLITUDE of the wave to INCREASE.
E. BEATS
This is a special type of wave interference that causes a variation in LOUDNESS.
Two sound waves with slightly different
frequency.
The sum is a beat wave. Its frequency is
the average of the two uncombined waves
and the amplitude (loudness) changes with
the constructive and destructive interference
pattern.
15