Sound
Chapter 12
Sound Waves
!   Sound waves are produced by vibrations.
!   With vibration, the air molecules are pushed together
and spread apart.
!   A region of high molecular density and high air
pressure is called a compression.
!   A region of lower molecular density and low air
pressure is called a rarefaction.
Sound Waves
!   Compressions and rarefactions caused by vibrations
occur in a periodic fashion. When an object vibrates
in harmonic motion, the air molecules also vibrate in
harmonic motion.
!   The vibrations are parallel to the direction of the
wave’s motion.
!   Remind me to bring a slinky tomorrow.
Sound Waves
!   Like other periodic functions, sound waves have
frequency. The frequency is the number of cycles per
unit of time.
!   Frequencies in the audible range for humans are
between 20 Hz and 20,000 Hz.
!   The frequency of a sound wave determines a sound’s
pitch, or how high or low we perceive the sound to be.
!   Higher frequencies have higher pitches.
Sound Waves
!   Like other periodic functions, sound waves have
frequency. The frequency is the number of cycles per
unit of time.
!   Frequencies in the audible range for humans are
between 20 Hz and 20,000 Hz.
!   The frequency of a sound wave determines a sound’s
pitch, or how high or low we perceive the sound to be.
!   Higher frequencies have higher pitches.
Sound Waves
!   The motion of a sound wave can change when it
interacts with materials of different densities.
!   The speed of sound depends on the medium through
which it travels.
!   The density of the substance depends on its chemical
composition, phase, and temperature.
Sound Waves
!   Sound waves propagate in three dimensions.
!   Spherical waves can be represented by concentric
circles.
Sound Waves
!   The Doppler Effect: When a sound source passes an
observer, the pitch will change.
!   This is because of RELATIVITY! J
!   As the sound source approaches, each new
compression originates closer and closer to the
observer, so they frequency is perceived higher.
!   As the sound source departs, each new compression
originates farther and farther from the observer, and
the frequency is perceived as lower.
Sound Waves
!   A stationary sound source also changes pitch when
perceived by a moving observer. As the observer
approaches, he or she encounters the compressions
faster. As he or she departs, it takes the sound waves
longer to catch up.
Sound Intensity and
Resonance
!   Intensity is the rate of energy flow through a given area.
As spherical waves get farther and farther from their
source, they can be approximated as planar waves. We
look at a unit area of the plane wave when considering
intensity.
!   Power, P , is defined as the rate of energy transfer, so
intensity can also be described in terms of power.
Sound Intensity and
Resonance
!   The unit for power is the watt. Per area, the unit will
be watts per square meter (W/m2).
!   In a spherical wave, the power emitted by the source is
distributed over a spherical surface.
!   Surface area of a sphere: 4πr2
!   For a spherical wave, then,
Sample Problem A
Practice A Page 415
Sound Intensity and
Resonance
!   Both the frequency and the intensity of a sound are
factors in whether a sound is audible or not.
!   At lower intensities, we find the threshold of hearing.
!   At higher intensities, we find the threshold of pain.
Sound Intensity and
Resonance
!   Both the frequency and the intensity of a sound are
factors in whether a sound is audible or not.
Sound Intensity and
Resonance
!   Relative intensity is measured in decibels.
!   This is a logarithmic scale.
!   The threshold of hearing is at 0 dB. This intensity is
1.0x10-12.
!   The threshold of pain is at 120 dB. This intensity is
1.0x100.
Sound Intensity and
Resonance
!   Vibrations can be passed from one substance to
another.
!   For example, on a guitar, the vibration of the strings
force a vibration in the bridge and then in the guitar’s
body.
!   These forced vibrations are called sympathetic
vibrations.
Sound Intensity and
Resonance
!   Vibrations at an object’s natural frequency produce
resonance.
!   Another word for this is an object’s resonant frequency.
!   The amplitude of the vibrations will increase!
Harmonics
!   When a string is fixed at both ends and set into
vibration, you can get a variety of standing waves.
!   Nodes stay still and don’t move.
!   The distance from one node to the next is half of the
wavelength, so the string has to be at least that long.
Harmonics
!   Length of the string L:
!   L=λ/2 where the Greek letter lambda (λ) stands for
the wavelength.
!   The speed of the wave equals the frequency times the
wavelength. v=fλ
!   Thus we can find the fundamental frequency of a
vibrating string by f1=v/λ or f1=v/2L
Harmonics
!   Harmonics are integral multiples of the fundamental
frequency.
!   f2=2f1 is the second harmonic
!   f3=3f1 is the third harmonic
!   f4=4f1 is the fourth harmonic
!
fn=nv/2L is the general form for the nth harmonic
Harmonics
!   Standing waves can exist in a tube of gas.
!   We can use similar equations as previously, with L
being the length of the column of air instead of the
length of a string.
!   When both ends of a tube are open, the harmonic
series has the exact same equation. However, the ends
of the pipes are antinodes, rather than nodes.
Harmonics
!   When one end of a tube is open and the other isn’t,
the harmonic series changes because the closed end of
the pipe is always a node.
!   Because of this, only the ODD harmonics are possible
in these types of pipes!
!   λ1=4L
!   f1=v/4L
!
fn=nv/4L
Sample Problem B
Practice B page 427
Harmonics
!   The harmonics affect the sound quality, or timbre.
!   An instrument with several harmonics involved will
have a different sound quality than a tuning fork.
!   The fundamental frequency determines pitch.
Harmonics
!   A sound variation from a soft to loud and back to soft
is called a beat.
!   Beats per second corresponds to the difference in
frequency.
!   This is because of interference. In some places, there is
constructive interference. In other places, it’s
destructive.