UNIT 7
Waves, Vibrations, and
Sound
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Thursday February 2nd
WAVES, VIBRATIONS, AND SOUND
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TODAY’S AGENDA
Thursday, February 2
 More on Harmonics
 Problem Quiz #2
UPCOMING…
 Fri: Inertial Balance Lab
 Mon: Problem Quiz #3
 Tue: Speed of Sound Lab
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ConcepTest 14.12a Pied Piper I
You have a long pipe
(1) the long pipe
and a short pipe.
(2) the short pipe
Which one has the
(3) both have the same frequency
higher frequency?
(4) depends on the speed of sound
in the pipe
ConcepTest 14.12a Pied Piper I
You have a long pipe
(1) the long pipe
and a short pipe.
(2) the short pipe
Which one has the
(3) both have the same frequency
higher frequency?
(4) depends on the speed of sound
in the pipe
A shorter pipe means that the standing wave in the
pipe would have a shorter wavelength. Since the
wave speed remains the same, the frequency has
to be higher in the short pipe.
ConcepTest 14.12b Pied Piper II
A wood whistle has a variable
length. You just heard the tone
from the whistle at maximum
length. If the air column is made
shorter by moving the end stop,
what happens to the frequency?
1) frequency will increase
2) frequency will not change
3) frequency will decrease
ConcepTest 14.12b Pied Piper II
A wood whistle has a variable
length. You just heard the tone
from the whistle at maximum
length. If the air column is made
shorter by moving the end stop,
what happens to the frequency?
1) frequency will increase
2) frequency will not change
3) frequency will decrease
A shorter pipe means that the standing wave in the pipe would
have a shorter wavelength. Since the wave speed remains
the same, and since we know that v = f l, then we see that the
frequency has to increase when the pipe is made shorter.
ConcepTest 14.12c Pied Piper III
If you blow across the opening
of a partially filled soda bottle,
you hear a tone. If you take a big
sip of soda and then blow
across the opening again, how
will the frequency of the tone
change?
1) frequency will increase
2) frequency will not change
3) frequency will decrease
ConcepTest 14.12c Pied Piper III
If you blow across the opening
of a partially filled soda bottle,
you hear a tone. If you take a big
sip of soda and then blow
across the opening again, how
will the frequency of the tone
change?
1) frequency will increase
2) frequency will not change
3) frequency will decrease
By drinking some of the soda, you have effectively increased the
length of the air column in the bottle. A longer pipe means that
the standing wave in the bottle would have a longer wavelength.
Since the wave speed remains the same, and since we know that
v = f l, then we see that the frequency has to be lower.
Follow-up: Why doesn’t the wave speed change?
Chapter 12
Sound
Units of Chapter 12
•Characteristics of Sound
•Intensity of Sound: Decibels
•The Ear and Its Response; Loudness
•Sources of Sound: Vibrating Strings and Air
Columns
•Quality of Sound, and Noise; Superposition
•Interference of Sound Waves; Beats
•Doppler Effect
Units of Chapter 12
•Shock Waves and the Sonic Boom
•Applications: Sonar, Ultrasound, and Medical
Imaging
Standing Waves; String
The frequencies of the standing
waves on a particular string are called
resonant frequencies.
They are also referred to as the
fundamental and harmonics.
Standing Waves; Strings
The wavelengths and frequencies of standing waves are:
Standing Waves in Air Columns
• If one end of the air column is closed, a
node must exist at this end since the
movement of the air is restricted
• If the end is open, the elements of the air
have complete freedom of movement and
an antinode exists
Tube Open at Both Ends
Resonance in Air Column
Open at Both Ends
• In a pipe open at both ends, the natural
frequency of vibration forms a series
whose harmonics are equal to integral
multiples of the fundamental frequency
v
ƒn  n
 nƒ1
2L
n  1, 2, 3,
Tube Closed at One End
Resonance in an Air Column
Closed at One End
• The closed end must be a node
• The open end is an antinode
v
fn  n
 nƒ1
4L
n  1, 3, 5,
• There are no even multiples of the
fundamental harmonic
Beats
• Beats are alternations in loudness, due to
interference
• Waves have slightly different frequencies and the
time between constructive and destructive
interference alternates
• The beat frequency equals the difference in
frequency between the two sources:
ƒb  ƒ2  ƒ1
Quality of Sound – Tuning Fork
• Tuning fork
produces only the
fundamental
frequency
Quality of Sound – Flute
• The same note
played on a flute
sounds differently
• The second
harmonic is very
strong
• The fourth harmonic
is close in strength
to the first
Quality of Sound – Clarinet
• The fifth harmonic is
very strong
• The first and fourth
harmonics are very
similar, with the third
being close to them
Timbre
• In music, the characteristic sound of any
instrument is referred to as the quality of
sound, or the timbre, of the sound
• The quality depends on the mixture of
harmonics in the sound
Pitch
• Pitch is related mainly, although not
completely, to the frequency of the sound
• Pitch is not a physical property of the sound
• Frequency is the stimulus and pitch is the
response
– It is a psychological reaction that allows humans
to place the sound on a scale
Doppler Effect
As can be seen in the previous
image, a source moving toward an
observer has a higher frequency
and shorter wavelength; the
opposite is true when a source is
moving away from an observer.
Shock Waves and the Sonic Boom
If a source is moving faster than the wave
speed in a medium, waves cannot keep up and
a shock wave is formed.
The angle of the cone is:
(12-5)
Shock Waves and the Sonic Boom
Shock waves are analogous to the bow waves
produced by a boat going faster than the wave
speed in water.
Shock Waves and the Sonic Boom
Aircraft exceeding the speed of sound in air will
produce two sonic booms, one from the front
and one from the tail.
Applications:
Sonar, Ultrasound, and Medical Imaging
Sonar is used to locate objects underwater by
measuring the time it takes a sound pulse to
reflect back to the receiver.
Similar techniques can be used to learn about
the internal structure of the Earth.
Sonar usually uses ultrasound waves, as the
shorter wavelengths are less likely to be
diffracted by obstacles.
Applications:
Sonar, Ultrasound, and Medical Imaging
Ultrasound is also
used for medical
imaging. Repeated
traces are made
as the transducer
is moved, and a
complete picture
is built.
Applications:
Sonar, Ultrasound, and Medical Imaging
Ordinary ultrasound gives a good picture; highresolution ultrasound is excellent.
Summary of Chapter 12
• Sound is a longitudinal wave in a medium.
• The pitch of the sound depends on the
frequency.
• The loudness of the sound depends on the
intensity and also on the sensitivity of the ear.
• The strings on stringed instruments produce a
fundamental tone whose wavelength is twice the
length of the string; there are also various
harmonics present.
Summary of Chapter 12
• Wind instruments have a vibrating column of
air when played. If the tube is open, the
fundamental is twice its length; if it is closed the
fundamental is four times the tube length.
• Sound waves exhibit interference; if two
sounds are at slightly different frequencies they
produce beats.
• The Doppler effect is the shift in frequency of a
sound due to motion of the source or the
observer.
END
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