What is a wave?

A wave is the motion of a disturbance.
What is a wave?
The medium is the physical
environment through which a
disturbance can travel.
 A mechanical wave is a wave that
requires a medium.
 Some waves do not require a medium;
electromagnetic waves are an example
that we will study later.

Types of waves
Pulse wave: A wave that consists of a
single traveling pulse.
 Periodic wave: created by continuously
generated pulses from one end of the
rope.

Types of waves

A wave whose source vibrates with
simple harmonic motion is a sine wave.
Types of waves

A transverse wave is a wave whose
particles vibrate perpendicularly to the
direction the wave is traveling.
equilibrium
Wave Characteristics

Crest: the highest point above the
equilibrium position.
Wave Characteristics

Trough: the lowest point below the
equilibrium position.
Wave Characteristics

Wavelength: the distance between two
adjacent similar points of a wave
◦ crest to crest
◦ trough to trough
Wave Characteristics

Amplitude: the maximum displacement
from equilibrium.
◦ Crest to equilibrium
◦ Trough to equilibrium
Types of waves

A longitudinal wave is a wave whose
particles vibrate in parallel to the
direction the wave is traveling.
Types of waves
Wave characteristics

Wave speed
Wave characteristics
Waves transfer energy
 The rate of that transfer depends on the
amplitude at which the particles of the
medium are vibrating.

◦ The greater the amplitude, the more energy
the wave carries.

Damping occurs when that energy
diminishes over time.
◦ We disregard damping in many of our
problems.
Wave characteristics

The energy transferred is proportional
to the square of the wave’s amplitude
Wave Interference
Two waves can occupy the same space
at the same time.
 The overlapping of two waves is called
superposition.

Wave Interference

Displacements in the same direction:
constructive interference.
Wave Interference

Displacements in opposite direction:
destructive interference.
Wave Interference

What happens when waves hit a
boundary?
◦ Waves are reflected at a free boundary
◦ Waves are reflected and inverted at a fixed
boundary.
Wave Interference

A standing wave is a wave pattern that
results when two waves of the same
frequency, wavelength and amplitude
travel in opposite directions and
interfere.
◦ A node is a point in a standing wave that
maintains zero displacement.
◦ An antinode is a point in a standing wave
halfway between two notes at which the
largest displacement occurs.
Sound Wave Production
Sound waves are longitudinal.
 Compression: the region of a
longitudinal wave in which the density
and pressure are at a maximum.
 Rarefaction: The region of a
longitudinal wave in which the density
and pressure are at a minimum.

Sound Wave Production

Sound waves are longitudinal because
vibrations of air molecules are parallel
to the direction of wave motion.
Sound Wave Production

Tuning fork
Sound Wave Production

Tuning fork
Sound Wave Characteristics

Frequency (cycles per second)
◦ Low frequency = long wavelength
◦ High frequency = short wavelength
Sound Wave Characteristics

Pitch: a measure of how high or low a
sound is perceived to be, depending on
the frequency of the sound wave.
Sound Wave Characteristics

Sound can travel through solids, liquids
or gases.
◦ Waves consist of vibrating particles.
◦ Sound travels much more quickly through a
solid than a gas because the molecules are
closer together.
Sound Wave Characteristics
Sound Wave Characteristics
Sound speed depends upon the medium
as we just saw.
 Sound speed also depends upon the
temperature of the medium.
 As temperature increases, gas particles
collide more frequently so sound can
travel faster.
 Temperature has a negligible effect on
liquids or solids.

Sound Wave Characteristics
Sound waves propagate in three
dimensions.
 We assume a spherical wave front for
our purposes.

Wave fronts
** Distance between wave fronts
equals one wavelength
Standing Waves on a string
Standing Waves on a string

Fundamental frequency: the lowest
possible frequency of vibration of a
standing wave.
Standing Waves on a string
These frequencies form the harmonic series.
Standing Waves on a string

Harmonic series: a series of
frequencies that includes the
fundamental frequency and integral
multiples of the fundamental frequency.
Standing Waves on a string

Harmonic series of standing waves on
a vibrating string:
** Note: v is the speed of the waves on the string, not in the air.
Standing Waves in a pipe

If both ends of the pipe are open, all
harmonics are present.
v = the speed of sound in the pipe
L = length of pipe
Standing Waves in a pipe

If one ends of the pipe is closed, only
odd harmonics are present.
v = the speed of sound in the pipe
L = length of pipe
Standing Waves in a pipe

Beat: the periodic variation in the
amplitude of a wave that is the
superposition of two waves of slightsly
different frequencies.
Standing Waves in a pipe

The number of beats per second
corresponds to the difference between
frequencies.
◦ Two flute players could use beats to tune
their instrument. They would play the
same note and one flute would be adjusted
until no beats are heard, meaning the two
flutes would be in tune.
Sound Intensity

Intensity is the rate at which energy
flows through a unit area perpendicular
to the direction of wave motion.
Sound Intensity

Intensity of a spherical wave:
Sound Intensity

In combination, frequency and intensity
determine which sounds are audible.
Sound Intensity

Relative intensity: the ratio of the
intensity of a given sound wave to the
intensity at the threshold of hearing.
Sound Intensity
There is a logarithmic dependence of
perceived loudness on intensity.
 Loudness is measured according to a
decibel level.
 A decibel is a dimensionless unit that is
proportional to the log of a ratio using
the threshold of hearing.

Sound Intensity
Intensity (W/m2)
Decibel Level (dB)
Example
1.0x10-12
0
Threshold of hearing
1.0x10-11
10
Rustling leaves
1.0x10-10
20
Quiet whisper
1.0x10-9
30
Whisper
1.0x10-8
40
Mosquito buzzing
1.0x10-7
50
Normal conversation
1.0x10-6
60
Air conditioner at 6 m
1.0x10-5
70
Vacuum cleaner
1.0x10-4
80
Busy traffic
1.0x10-3
90
Lawn mower
1.0x10-1
110
Auto horn at 1 m
1.0x100
120
Threshold of pain
1.0x101
130
Machine gun
1.0x103
150
Jet plane
Resonance
Natural frequency: the frequency at
which a system tends to oscillate in the
absence of any driving or damping
force.
 Resonance: a phenomena that occurs
when the frequency of a force applied to
a system matches the natural frequency
of vibration of the system, resulting in a
large amplitude of vibration.

Resonance
Natural frequency: the frequency at
which a system tends to oscillate in the
absence of any driving or damping
force.
 Resonance: a phenomena that occurs
when the frequency of a force applied to
a system matches the natural frequency
of vibration of the system, resulting in a
large amplitude of vibration.
