Wave Motion and Sound
UCVTS AIT Physics
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Waves
•
Nature of Waves
– A wave is a disturbance that transfers energy from one place to another
without requiring any net flow of mass.
• mechanical waves require a medium (air, water, rock, etc.) in which to travel.
• Light, and other electromagnetic waves, do not require a medium; we'll deal with
those later in the semester.
– pulse and periodic waves
• A pulse is a single disturbance
• a periodic wave is a continually oscillating motion. There is a close connection
between simple harmonic motion and periodic waves; in most periodic waves, the
particles in the medium experience simple harmonic motion.
– Waves can also be separated into transverse and longitudinal waves.
• transverse wave
–
the motion of the particles of the medium is at right angles (i.e., transverse) to the
direction the wave moves.
• longitudinal wave
–
the particles oscillate along the direction of motion of the wave (sound waves )
– Surface waves, such as water waves, are generally a combination of a
transverse and a longitudinal wave. The particles on the surface of the
water travel in circular paths as a wave moves across the surface.
I can ride
this wave!
UCVTS AIT Physics
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Waves
• Types of Waves
– transverse wave
– longitudinal wave
UCVTS AIT Physics
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Waves
• Periodic Waves
– Cycles or patterns that are produced over and
over again are called periodic waves
1
T
T is period , f is frequency (in Hz )
speed of a wave v
f 
Transvers
e
wave

 f
T
 is wavelength
v
Snapshot at one time of the slinky
A single point on the slinky
One wave
cycle is
shaded area
UCVTS AIT Physics
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Waves
• Nature of Sound
– Sound is a longitudinal wave that is created by a
vibrating object
• Sound travels by compressing air
• Sound can be transmitted only in a medium such as gas,
liquid or solid
– No sound in space!
• In general sound travels faster through a more dense
material
– 4 times as fast through water than air
• Sound Intensity
– Example 6
I
P
A
W
I is in 2
m
UCVTS AIT Physics
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Waves
• Sound Intensity
– Decibels (dB)
• A measurement unit used for comparing two sound intensities (or
voltage, power, etc. levels)
• The human ear has an incredibly large range
– We are able to detect sound intensities from 1 x 10-12 W / m2 to 1 W / m2.
– A more convenient way to measure the loudness of sound is in decibels (dB);
in decibels, the range of human hearing goes from 0 dB to 120 dB. The ear
responds to the loudness of sound logarithmically, so the decibel scale is a
logarithmic scale:
 I 
  (10dB) log  
 I0 
• On the decibel scale, doubling the intensity corresponds to an increase
of 3 dB.
• For humans this 3dB increase does not correspond to a perceived
doubling of loudness
– We perceive loudness to be doubled when the intensity increases by a
factor of 10. This corresponds to a 10 dB increase. A change by 1 dB is
about the smallest change a human being can detect.
– Example 9
UCVTS AIT Physics
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Waves
•
Sound Intensity: Decibels (dB) and the ear
–
The decibel scale is used because it corresponds to how we
perceive the loudness of sounds.
•
The ear is split into three sections
– the outer ear
» The outer ear acts much like a funnel, collecting the sound and
transferring it inside the head down a passage that's about 3 cm
long, ending at the ear drum.
– the middle ear
» The middle ear is connected to the mouth via the eustachian
tubes to ensure that the inside of the eardrum is maintained at
atmospheric pressure. This is necessary for the drum to be able
to respond to the small variations in pressure from atmospheric
pressure that make up the sound wave.
» In the middle ear are three small bones, called the hammer,
anvil, and stirrup because of their shapes. These transfer the
sound wave from the ear drum to the inner ear. Similar to a
hydraulic lift, the pressure is transferred from a relatively
large area (the eardrum) to a smaller area (the window to the
inner ear). By Pascal's principle, the pressure is constant. The
force is smaller at the small-area inner ear, but the work
done at each end is equal, so the inner ear experiences a
vibration with a much larger amplitude than that at the ear
drum. The bones, in effect, act as an audio amplifier.
» The three bones in the middle ear are designed to transfer
sound energy from the eardrum to the inner ear without any
energy lost to reflections. The physics term for this is
"impedance match": any time energy is transferred from one
system to another without any reflected energy, the impedances
are matched at the transfer point...in this case, the bones
provide the impedance matching.
– the inner ear
» The inner ear contains a fluid-filled tube, the cochlea. The
cochlea is coiled like a snail, is about 3 mm in diameter, and is
divided along its length by the basilar membrane. It also
contains a set of hair cells that convert the sound wave into
electrical pulses; these are transferred along nerves to the
brain, to be interpreted as sound. When a sound signal enters
the inner ear, a small movement of the basilar membrane or the
fluid in the cochlea results in the rubbing of another membrane
across the hair cells. The relatively long hairs provide another
level of amplification, in the sense that a small force applied at
the ends is converted into a relatively large torque
UCVTS AIT Physics
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Waves
• Doppler Effect
– The Doppler effect describes the shift in the frequency of a wave
sound when the wave source and/or the receiver is moving.
• the Doppler effect applies to any kind of wave. As with ultrasound, the
Doppler effect has a variety of applications, ranging from medicine
(with sound) to police radar and astronomy (with electromagnetic
waves).
– If you hear an emergency vehicle with its siren on, you notice an
abrupt change in the frequency of the siren when it goes past you.
• If you are standing still when the vehicle is coming toward you, the
frequency is higher than it would be if the vehicle was stationary
• when the vehicle moves away from you, the frequency is lower.
UCVTS AIT Physics
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Waves
• Doppler Effect
– General case Doppler Effect equation
 vo
1


v
fo  f s 
vs
1 
v






UCVTS AIT Physics
Vo is observer
Vs is source
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Waves
Doppler Effect
•
Real World Applications
Doppler blood flow meter. This
device measures the speed of
blood flow using transmitting
and receiving elements that are
placed on the skin. The Doppler
flow meter can be used to
locate regions where blood
vessels have narrowed.
NEXRAD weather radar. The
color enhanced view of a
tornado shows winds moving
toward (green) and away (red)
from a NEXRAD station, which
is below and to the right of the
figure. The white dot and arrow
indicate the storm center and
direction of wind circulation
UCVTS AIT Physics
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Waves
•
Interference
– Interference is what happens when two or more waves come together
• Depending on how the peaks and troughs of the waves are matched up
–
–
•
the waves might add together or
they can partially or even completely cancel each other. The concept of interference
applies to sound waves, and all waves.
Linear Superposition
– when two or more waves come together, the result is the sum of the
individual waves.
– The principle of linear superposition applies to any number of waves
• consider what happens when two waves come together. This could be sound
reaching you simultaneously from two different sources, or two pulses traveling
towards each other along a string. When the waves come together, what happens?
The result is that the waves are superimposed: they add together, with the
amplitude at any point being the addition of the amplitudes of the individual waves
at that point.
– Although the waves interfere with each other when they meet, they
continue traveling as if they had never encountered each other. When the
waves move away from the point where they came together, in other words,
their form and motion is the same as it was before they came together.
UCVTS AIT Physics
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Waves
•
Interference
– Constructive
• Constructive interference occurs whenever waves come together so that they are
in phase with each other. This means that their oscillations at a given point are in
the same direction, the resulting amplitude at that point being much larger than
the amplitude of an individual wave. For two waves of equal amplitude interfering
constructively, the resulting amplitude is twice as large as the amplitude of an
individual wave. For 100 waves of the same amplitude interfering constructively,
the resulting amplitude is 100 times larger than the amplitude of an individual
wave. Constructive interference, then, can produce a significant increase in
amplitude.
• The following diagram shows two pulses coming together, interfering
constructively, and then continuing to travel as if they'd never encountered each
other.
UCVTS AIT Physics
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Waves
•
Interference
– Destructive
• Destructive interference occurs when waves come together in such a way that
they completely cancel each other out. When two waves interfere destructively,
they must have the same amplitude in opposite directions. When there are more
than two waves interfering the situation is a little more complicated; the net
result, though, is that they all combine in some way to produce zero amplitude. In
general, whenever a number of waves come together the interference will not be
completely constructive or completely destructive, but somewhere in between. It
usually requires just the right conditions to get interference that is completely
constructive or completely destructive.
• The following diagram shows two pulses interfering destructively. Again, they
move away from the point where they combine as if they never met each other.
UCVTS AIT Physics
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Waves
• Beats
– Periodic variations in amplitude that arise from
the linear superposition of two waves that have
slightly different frequencies
– With sound waves the variation in amplitude cause
the loudness to vary at the beat frequency
• The beat frequency is the difference between the 2
source frequencies ƒbeat = |ƒ1 – ƒ2|
Yeah, I’m a
rock star,
because I tune
my guitar with
BEATS
UCVTS AIT Physics
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