Chapter 7
Waves and Sound
What is wave?
A wave is a disturbance that propagates from one place to another. Or simply, it
carries energy from place to place.
The easiest type of wave to visualize is a transverse wave, where the
displacement of the medium is perpendicular to the direction of motion of the
wave.
Types of waves
• Transverse Wave
the displacement of the string
element is normal to the
direction of wave motion
Walker, Physics, 3rd edition
• Longitudinal Wave
The displacement of the spring element is along the direction of
wave motion
• Water waves
Water waves are a combination of
transverse and longitudinal waves.
Water waves are partially transverse and partially longitudinal
What is sound?
• Sound is a kind of longitudinal wave that consists of density waves.
• The displacement of particles in the medium is along the direction of wave
motion.
• Patterns of compressions and rarefactions that travel outward rapidly from
their source.
Sound Waves
• When a sound passes, the air pressure in your ear fluctuates up and down
about normal atmospheric pressure.
• When the fluctuations are repetitive, you hear a tone with a pitch equal to
the fluctuation’s frequency. Strictly speaking, pitch is an auditory sensation
to compare the higher and lower frequency.
• Audible frequencies ranging between approximately 20 Hz to 20 000 Hz.
• For some people who have musically trained, are capable of detecting a
difference in frequency between two separate sounds that is as little as 2 Hz.
• When two sounds with a frequency difference of greater than 7 Hz are
played simultaneously, most people are capable of detecting the presence
of a complex wave pattern resulting from them.
Pressure and Density for standing sound wave (1)
Source: http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html
Pressure and Density for standing sound wave (2)
Source: http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html
Pressure and Density for standing sound wave (3)
Source: http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html
Pressure and Density for standing sound wave (4)
Source: http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html
Pressure and Density for sound wave (5)
Pressure
The distance between adjacent
condensations is equal to the
wavelength of the sound wave.
In the drawing, one cycle is shaded in color.
• The amplitude A is the maximum excursion of a particle of the medium
from the particles undisturbed position.
• The wavelength is the horizontal length of one cycle of the wave.
• The period is the time required for one complete cycle.
• The frequency is related to the period and has units of Hz, or s-1.
1
f =
T
Waves Traveling on Guitar Strings
Transverse waves travel on each string of an electric guitar after the
string is plucked.
High pitched string
- low density string, i.e. thinner string
Low pitched string
– high density string, i.e. thicker string
Wave Speed Versus Particle Speed
The Frequency of a Sound Wave
The frequency is the number of cycles per second.
A sound with a single frequency is called a pure tone.
The brain interprets the frequency in terms of the subjective quality
called pitch.
THE PRESSURE AMPLITUDE OF A SOUND WAVE
Loudness is an attribute of
a sound that depends primarily
on the pressure amplitude
of the wave. On the other hands,
It is subjective. Each individual
determines what is loud,
depending on the acuteness of
his or her hearing.
Speed of Sound in Gases, Liquids, and Solids
Lightning, Thunder, and a Rule of Thumb
There is a rule of thumb for estimating how far away a thunderstorm is.
After you see a flash of lighting, count off the seconds until the thunder
is heard. Divide the number of seconds by five. The result gives the
approximate distance (in miles) to the thunderstorm. Why does this
rule work?
Sound Intensity
Sound waves carry energy that can be used to do work.
The amount of energy transported per second is called the
power of the wave.
The sound intensity is defined as the power that passes perpendicularly
through a surface divided by the area of that surface.
P
I=
A
Sound Intensity
The smallest sound intensity that the human ear can detect is
about 1x10-12W/m2. This intensity is called the threshold of hearing.
On the other extreme, continuous exposure to intensities greater than
1W/m2 can be painful.
power of sound source
P
I=
4π r 2
area of sphere
Reflected Sound and Sound Intensity
Suppose the person singing in the shower produces a sound power. Sound
reflects from the surrounding shower stall.
At a distance r in front of the person, the sound intensity (power per unit area)
is greater because there are reflected sound waves.
Decibels
The decibel (dB) is a measurement unit used when comparing two sound
intensities.
Because of the way in which the human hearing mechanism responds to
intensity, it is appropriate to use a logarithmic scale called the intensity
level:
I
β = (10 dB) log
Io
I o = 1.00 ×10 −12 W m 2
Note that log(1)=0, so when the intensity
of the sound is equal to the threshold of
hearing, the intensity level is zero.
Typical Sound Intensities and Intensity Levels
Relative to the Threshold of Hearing
The Doppler Effect
The Doppler effect is the
change in frequency or pitch
of the sound detected by
an observer because the sound
source and the observer have
different velocities with respect
to the medium of sound
propagation.
v = fλ
𝒗𝒗
⇒ f=
𝝀𝝀
MOVING SOURCE
Source moving
toward a stationary Higher frequency
observer
Source moving Lower frequency
away from a stationary
observer
MOVING OBSERVER
v = fλ
𝒗𝒗
⇒ f=
𝝀𝝀
Observer moving Higher frequency
towards stationary
source
Observer moving
away from Lower frequency
stationary source
Sonic Boom
Sonic Boom and Mach Cone
Vsource / Vsound < 1 Vsource / Vsound = 1
A Mach cone
Vsource / Vsound > 1
Doppler Effect of Light
Doppler Effect of Light
Applications of Sound in Medicine
By scanning ultrasonic waves across the body and detecting the echoes
from various locations, it is possible to obtain an image.
Cavitron Ultrasonic Surgical Aspirator (CUSA)
Ultrasonic sound waves cause
the tip of the probe to vibrate at
23 kHz and shatter sections of
the brain tumor that it touches.
The probe is small that it will not
damage the surrounding healthy
tissue.
The fragments are flushed out of
the brain with a saline solution.
Doppler flow meter
When the sound is reflected
from the red blood cells, its
frequency is changed in a
kind of Doppler effect because
the cells are moving.
From the flow speed, it
determines the region that the
blood vessels has narrowed.
Resonance
During the resonance, the
amplitude of the oscillation
increases dramatically when the
frequency of the driven force is
near the natural frequency of the
system.
The natural frequency is called the
resonance frequency of the
system.
Resonance
Demonstration
Resonance
Playing the swing is an example of resonance.
Resonance
Investigate how the player swings to a higher altitude
Constructive and Destructive Interference of Sound Waves
When two waves always meet condensation-to-condensation and
rarefaction-to-rarefaction, they are said to be exactly in phase and
to exhibit constructive interference.
Constructive and Destructive Interference of Sound Waves
When two waves always meet condensation-to-rarefaction, they are
said to be exactly out of phase and to exhibit destructive interference.
Constructive and Destructive Interference of Sound Waves
Diffraction
The bending of a wave around
an obstacle or the edges of an
opening is called diffraction.
For the diffraction of sound, the
wavelength of sound and the
size of door is comparable.
The listener, who is not staying
directly outside the room, can
hear the sound.
Beats
The beat frequency is the difference between the two sound
frequencies.
Beats
The beat frequency is the difference between the two sound
frequencies.
