Chapter06
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Chapter 6
Waves and Sound
2
3
4
5
6
Waves — types and properties A wave is a traveling disturbance consisting
of coordinate vibrations that transmit energy with no net movement of matter. The disturbance is frequently called an oscillation or vibration. The substance through which the wave travels is called the medium.
7
Waves — types and properties, cont’d There are two main wave types:
Transverse waves have oscillations that are perpendicular (transverse) to the direction the wave travels.
Examples include waves on a rope, electromagnetic waves and some seismic waves.
Longitudinal waves have oscillations that are along the direction the wave travels.
Examples include sound and some seismic waves. 8
Waves — types and properties, cont’d This figure illustrates the two main types of
waves.
9
Waves — types and properties, cont’d Consider a string of length l and mass m. The speed at which a wave travels on the
string when it is under a tension T is
T v= . ρ
ρ is the mass per unit length:
m ρ= . l
10
Waves — types and properties, cont’d From this we see that the speed:
Increases as the tension increases.
Is faster for smaller strings.
The string has a greater restoring force that attempts to straighten it out. The string has less mass that has to be moved by the restoring force.
Is independent of the length.
The speed depends on the mass per length, not on just the length. 11
Example Example 6.1 A student stretches a Slinky out on the floor to a length of 2 meters. The force needed to keep the Slinky stretched in measured and found to be 1.2 newtons. The Slinky’s mass is 0.3 kilograms. What is the speed of any wave sent down the Slinky by the student?
12
Example Example 6.1 ANSWER: The problem gives us:
l=2m F = 1.2 N m = 0.3 kg
The linear mass density is
m 0.3 kg ρ= = = 0.15 kg/m l 2m 13
Example Example 6.1 ANSWER: The wave speed is then
v=
F 1.2 N = = 2.8 m/s. ρ 0.15 kg/m
14
Waves — types and properties, cont’d The speed of a sound wave when the air is at
a temperature T is
v = 20.1× T .
The temperature must be in Kelvin.
15
Example Example 6.2 What is the speed of sound in air at room temperature (20ºC = 68ºF)?
16
Example Example 6.2 ANSWER: The problem gives us:
T = 20º C
We need to convert this temperature from celsius to kelvin:
T = 20 + 273 = 293 K
The sound speed is then
v = 20.1 × 293 = 344 m/s 17
Example Example 6.2 DISCUSSION: The factor of 20.1 depends on the properties of air. For other gases:
Helium:
v = 58.8 × T .
Carbon dioxide:
v = 15.7 × T . 18
Waves — types and properties, cont’d The amplitude of a wave is the maximum
displacement of the wave from the equilibrium position.
It is just the distance equal to the height of a peak or the depth of a valley.
19
Waves — types and properties, cont’d The wavelength is the distance between
successive “like” points on a wave.
“Like” points might be peaks, valleys, etc.
The wavelength is denoted by the Greek
letter lambda: λ .
20
Waves — types and properties, cont’d Here is an illustration of
changing the wavelength and/or amplitude. Lower amplitude implies smaller height/depth. Shorter wavelength implies more complete waves “fit” in a given distance.
21
Waves — types and properties, cont’d The frequency of a wave indicates the
number of cycles of a wave that pass a given point per unit time.
It is the number of oscillations per second.
22
Waves — types and properties, cont’d We use different terminology for the “peaks”
and “valleys” of a longitudinal wave.
A compression is where the medium is squeezed together. A expansion is where the medium is spread apart.
23
Waves — types and properties, cont’d The wavelength and frequency are related to
the wave speed according to:
v = f λ.
v is the wave’s speed, f is the wave’s frequency, and λ is the wave’s wavelength.
24
Example Example 6.3 Before a concert, musicians in an orchestra tune their instruments to the note A, which has a frequency of 440 Hz. What is the wavelength of this sound in air at room temperature? The speed of sound at this temperature is 344 m/s.
25
Example Example 6.3 ANSWER: The problem gives us:
f = 440 Hz v = 344 m/s
The relation between frequency, wavelength and wave speed is
v= fλ
The wavelength is then
v 344 m/s λ= = = 0.78 m f 440 Hz
26
Waves — types and properties, cont’d A complex wave is any continuous wave that
does not have a sinusoidal shape.
27
Aspects of wave propagation There are two approaches to represent a
wave. A wavefront is a circle representing the location of a wave peak. A ray is an arrow representing the direction that a wave segment is traveling.
28
29
Aspects of wave propagation, cont’d A reflection is when a wave abruptly changes
direction. A wave is reflected whenever it reaches a boundary of its medium or encounters an abrupt change in the properties of its medium.
30
Aspects of wave propagation, cont’d We can use either model to
examine reflection from a flat mirror. The point behind the mirror from which the reflection appears to originate is called the image.
31
Aspects of wave propagation, cont’d For a curved surface, the reflections can be
focused to a point.
Examples include satellite dishes, radar receivers, etc.
32
33
Aspects of wave propagation, cont’d The Doppler effect is an apparent change in a
wave’s wavelength due to the relative motion between the source and receiver. Consider a source emitting waves and moving to the right.
The crests appear closer together in the direction the source moves.
34
Aspects of wave propagation, cont’d
The crests appear farther apart in the direction opposite to the source’s motion.
These changes cause
the frequency to sound different since the wave travels at the same speed relative to the medium.
35
Aspects of wave propagation, cont’d A shock wave occurs whenever the speed of
the source is greater than the wave speed. The medium cannot respond fast enough to propagate the wave.
The crests essentially “pile up” in front of the source.
This build-up causes a large-amplitude pulse.
This produces a sonic boom for supersonic aircraft. A fast boat creates a bow wave. 36
Aspects of wave propagation, cont’d Watching the waves expand from the source
over time, we can construct a leading edge for the shock wave.
The angle of this leadingedge was an important discovery for jet-planes.
37
Aspects of wave propagation, cont’d Diffraction results whenever a wave has to
travel past a barrier or obstruction. As the wave travels through the opening, the outgoing waves bend. The amount of diffraction depends on the wavelength and the size of the obstruction.
38
Aspects of wave propagation, cont’d When the opening is much larger than the
wavelength, there is little diffraction. The amount of diffraction increases as the wavelength becomes more similar to the size of the opening.
39
Aspects of wave propagation, cont’d Diffraction explains why you
can hear a sound through a door even if you’re behind a wall.
The sound’s wavelength is much longer than the size of the door, so the sound wave bends around the wall.
40
Aspects of wave propagation, cont’d Interference occurs whenever two or more
waves overlap.
41
Aspects of wave propagation, cont’d When the waves
interfere to create a larger amplitude, we call it constructive interference. When the waves interfere to reduce the amplitude, it is called destructive interference. 42
Sound The speed of sound in a substance depends
on: the mass of its constituent atoms, and the strength of the forces between the atoms.
The speed of sound is large when:
the atoms have small mass — they’re easier to move, and/or the forces between the atoms are larger — an atom pushes harder on its neighbor.
43
Sound, cont’d Typically we represent a sound wave as a
transverse wave (even though it is not). A region of compression is drawn as a crest. A region of expansion is drawn as a trough.
44
Sound, cont’d A waveform of a sound
wave is a graph of the air-pressure fluctuations causes by the sound wave versus time. A pure tone is a sound with a sinusoidal waveform. A complex wave is a sound that is not pure.
45
Sound, cont’d Noise is sound that has a random waveform.
It does not have a definite wavelength or period.
Sound with frequencies below our audible
range is called infrasound.
Below about 20 Hz.
Sound with frequencies above our audible
range is called ultrasound.
Above about 20,000 Hz. 46
Production of sound Sound can be produced by:
Causing a body to vibrate:
Varying an air flow:
e.g., buzzing your lips.
Abrupt changes in an object’s temperature:
e.g., plucking a string.
e.g., a lightning flash creates thunder.
By creating a shock wave:
e.g., flying faster than the speed of sound. 47
Perception of sound We have to be careful when we discuss
sound. There are physical properties we can measure. But our ears do not just measure these physical properties. We have to deal with the perception of the sound.
48
Perception of sound, cont’d Pitch is the perception of highness or
lowness of a sound. The pitch depends primarily on the frequency of the sound. It also depends on the duration.
A very short sound might sound like a click even if it has a definite frequency.
49
Perception of sound, cont’d Loudness is the perception of whether a
sound is easy to hear or painful to hear. It depends primarily on the amplitude of the sound. It also depends on whether the sound is played with other sounds (before, after, concurrently, etc). It even depends on the frequency.
Our ears are more sensitive to higher frequencies and less sensitive to lower frequencies. 50
Perception of sound, cont’d Our eardrums respond to sound pressure
level.
A louder sound creates a larger compression, i.e., higher pressure, than a quiet sound.
We typically call the sound pressure level just
the sound level. It is measured in decibels (dB). 0 dB corresponds to inaudible. Normal conversation is about 50 dB. ~120 dB starts causing pain.
51
Perception of sound, cont’d The sound level of the quietest sound is
called the threshold of hearing. The sound level at which we start experiencing pain is called the threshold of pain. The minimum increase in sound level that is noticeable is about 1 dB. For a sound to be judged as “twice as loud,” the original sound must be increased by 10 dB. 52
Waves and Sound
2
3
4
5
6
Waves — types and properties A wave is a traveling disturbance consisting
of coordinate vibrations that transmit energy with no net movement of matter. The disturbance is frequently called an oscillation or vibration. The substance through which the wave travels is called the medium.
7
Waves — types and properties, cont’d There are two main wave types:
Transverse waves have oscillations that are perpendicular (transverse) to the direction the wave travels.
Examples include waves on a rope, electromagnetic waves and some seismic waves.
Longitudinal waves have oscillations that are along the direction the wave travels.
Examples include sound and some seismic waves. 8
Waves — types and properties, cont’d This figure illustrates the two main types of
waves.
9
Waves — types and properties, cont’d Consider a string of length l and mass m. The speed at which a wave travels on the
string when it is under a tension T is
T v= . ρ
ρ is the mass per unit length:
m ρ= . l
10
Waves — types and properties, cont’d From this we see that the speed:
Increases as the tension increases.
Is faster for smaller strings.
The string has a greater restoring force that attempts to straighten it out. The string has less mass that has to be moved by the restoring force.
Is independent of the length.
The speed depends on the mass per length, not on just the length. 11
Example Example 6.1 A student stretches a Slinky out on the floor to a length of 2 meters. The force needed to keep the Slinky stretched in measured and found to be 1.2 newtons. The Slinky’s mass is 0.3 kilograms. What is the speed of any wave sent down the Slinky by the student?
12
Example Example 6.1 ANSWER: The problem gives us:
l=2m F = 1.2 N m = 0.3 kg
The linear mass density is
m 0.3 kg ρ= = = 0.15 kg/m l 2m 13
Example Example 6.1 ANSWER: The wave speed is then
v=
F 1.2 N = = 2.8 m/s. ρ 0.15 kg/m
14
Waves — types and properties, cont’d The speed of a sound wave when the air is at
a temperature T is
v = 20.1× T .
The temperature must be in Kelvin.
15
Example Example 6.2 What is the speed of sound in air at room temperature (20ºC = 68ºF)?
16
Example Example 6.2 ANSWER: The problem gives us:
T = 20º C
We need to convert this temperature from celsius to kelvin:
T = 20 + 273 = 293 K
The sound speed is then
v = 20.1 × 293 = 344 m/s 17
Example Example 6.2 DISCUSSION: The factor of 20.1 depends on the properties of air. For other gases:
Helium:
v = 58.8 × T .
Carbon dioxide:
v = 15.7 × T . 18
Waves — types and properties, cont’d The amplitude of a wave is the maximum
displacement of the wave from the equilibrium position.
It is just the distance equal to the height of a peak or the depth of a valley.
19
Waves — types and properties, cont’d The wavelength is the distance between
successive “like” points on a wave.
“Like” points might be peaks, valleys, etc.
The wavelength is denoted by the Greek
letter lambda: λ .
20
Waves — types and properties, cont’d Here is an illustration of
changing the wavelength and/or amplitude. Lower amplitude implies smaller height/depth. Shorter wavelength implies more complete waves “fit” in a given distance.
21
Waves — types and properties, cont’d The frequency of a wave indicates the
number of cycles of a wave that pass a given point per unit time.
It is the number of oscillations per second.
22
Waves — types and properties, cont’d We use different terminology for the “peaks”
and “valleys” of a longitudinal wave.
A compression is where the medium is squeezed together. A expansion is where the medium is spread apart.
23
Waves — types and properties, cont’d The wavelength and frequency are related to
the wave speed according to:
v = f λ.
v is the wave’s speed, f is the wave’s frequency, and λ is the wave’s wavelength.
24
Example Example 6.3 Before a concert, musicians in an orchestra tune their instruments to the note A, which has a frequency of 440 Hz. What is the wavelength of this sound in air at room temperature? The speed of sound at this temperature is 344 m/s.
25
Example Example 6.3 ANSWER: The problem gives us:
f = 440 Hz v = 344 m/s
The relation between frequency, wavelength and wave speed is
v= fλ
The wavelength is then
v 344 m/s λ= = = 0.78 m f 440 Hz
26
Waves — types and properties, cont’d A complex wave is any continuous wave that
does not have a sinusoidal shape.
27
Aspects of wave propagation There are two approaches to represent a
wave. A wavefront is a circle representing the location of a wave peak. A ray is an arrow representing the direction that a wave segment is traveling.
28
29
Aspects of wave propagation, cont’d A reflection is when a wave abruptly changes
direction. A wave is reflected whenever it reaches a boundary of its medium or encounters an abrupt change in the properties of its medium.
30
Aspects of wave propagation, cont’d We can use either model to
examine reflection from a flat mirror. The point behind the mirror from which the reflection appears to originate is called the image.
31
Aspects of wave propagation, cont’d For a curved surface, the reflections can be
focused to a point.
Examples include satellite dishes, radar receivers, etc.
32
33
Aspects of wave propagation, cont’d The Doppler effect is an apparent change in a
wave’s wavelength due to the relative motion between the source and receiver. Consider a source emitting waves and moving to the right.
The crests appear closer together in the direction the source moves.
34
Aspects of wave propagation, cont’d
The crests appear farther apart in the direction opposite to the source’s motion.
These changes cause
the frequency to sound different since the wave travels at the same speed relative to the medium.
35
Aspects of wave propagation, cont’d A shock wave occurs whenever the speed of
the source is greater than the wave speed. The medium cannot respond fast enough to propagate the wave.
The crests essentially “pile up” in front of the source.
This build-up causes a large-amplitude pulse.
This produces a sonic boom for supersonic aircraft. A fast boat creates a bow wave. 36
Aspects of wave propagation, cont’d Watching the waves expand from the source
over time, we can construct a leading edge for the shock wave.
The angle of this leadingedge was an important discovery for jet-planes.
37
Aspects of wave propagation, cont’d Diffraction results whenever a wave has to
travel past a barrier or obstruction. As the wave travels through the opening, the outgoing waves bend. The amount of diffraction depends on the wavelength and the size of the obstruction.
38
Aspects of wave propagation, cont’d When the opening is much larger than the
wavelength, there is little diffraction. The amount of diffraction increases as the wavelength becomes more similar to the size of the opening.
39
Aspects of wave propagation, cont’d Diffraction explains why you
can hear a sound through a door even if you’re behind a wall.
The sound’s wavelength is much longer than the size of the door, so the sound wave bends around the wall.
40
Aspects of wave propagation, cont’d Interference occurs whenever two or more
waves overlap.
41
Aspects of wave propagation, cont’d When the waves
interfere to create a larger amplitude, we call it constructive interference. When the waves interfere to reduce the amplitude, it is called destructive interference. 42
Sound The speed of sound in a substance depends
on: the mass of its constituent atoms, and the strength of the forces between the atoms.
The speed of sound is large when:
the atoms have small mass — they’re easier to move, and/or the forces between the atoms are larger — an atom pushes harder on its neighbor.
43
Sound, cont’d Typically we represent a sound wave as a
transverse wave (even though it is not). A region of compression is drawn as a crest. A region of expansion is drawn as a trough.
44
Sound, cont’d A waveform of a sound
wave is a graph of the air-pressure fluctuations causes by the sound wave versus time. A pure tone is a sound with a sinusoidal waveform. A complex wave is a sound that is not pure.
45
Sound, cont’d Noise is sound that has a random waveform.
It does not have a definite wavelength or period.
Sound with frequencies below our audible
range is called infrasound.
Below about 20 Hz.
Sound with frequencies above our audible
range is called ultrasound.
Above about 20,000 Hz. 46
Production of sound Sound can be produced by:
Causing a body to vibrate:
Varying an air flow:
e.g., buzzing your lips.
Abrupt changes in an object’s temperature:
e.g., plucking a string.
e.g., a lightning flash creates thunder.
By creating a shock wave:
e.g., flying faster than the speed of sound. 47
Perception of sound We have to be careful when we discuss
sound. There are physical properties we can measure. But our ears do not just measure these physical properties. We have to deal with the perception of the sound.
48
Perception of sound, cont’d Pitch is the perception of highness or
lowness of a sound. The pitch depends primarily on the frequency of the sound. It also depends on the duration.
A very short sound might sound like a click even if it has a definite frequency.
49
Perception of sound, cont’d Loudness is the perception of whether a
sound is easy to hear or painful to hear. It depends primarily on the amplitude of the sound. It also depends on whether the sound is played with other sounds (before, after, concurrently, etc). It even depends on the frequency.
Our ears are more sensitive to higher frequencies and less sensitive to lower frequencies. 50
Perception of sound, cont’d Our eardrums respond to sound pressure
level.
A louder sound creates a larger compression, i.e., higher pressure, than a quiet sound.
We typically call the sound pressure level just
the sound level. It is measured in decibels (dB). 0 dB corresponds to inaudible. Normal conversation is about 50 dB. ~120 dB starts causing pain.
51
Perception of sound, cont’d The sound level of the quietest sound is
called the threshold of hearing. The sound level at which we start experiencing pain is called the threshold of pain. The minimum increase in sound level that is noticeable is about 1 dB. For a sound to be judged as “twice as loud,” the original sound must be increased by 10 dB. 52
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