VIBRATION AND WAVES
Sound and Light
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Pendulum
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Pendulum’s Period:
The time required for one complete
vibration, for example, from one crest
to the next crest, is called the
pendulum's period and is measured in
seconds. The formula to calculate this
quantity is
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The formula to calculate this
quantity is:
where
•L is the length of the pendulum in
meters
•g is the gravitational field strength, or
acceleration due to gravity
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FREQUENCY:
The frequency of a pendulum
represents the number of vibrations per
second. This quantity is measured in
hertz (hz) and is the reciprocal of the
pendulum's period.
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EXAMPLE 1
What Would Be the Period of a
Pendulum Located at Sea Level If It Is
1.5 Meters Long?
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Solution 1
2.46 seconds
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EXAMPLE 2
If the pendulum's length were to
be shortened to one-fourth its
original value, what would be its
new period?
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SOLUTION 2
1.23 Seconds:
Since a simple pendulum's period is
proportional to the square root of its length
cutting the length to one-fourth of its original
value would result in the period being reduced
to one-half of its original value, or 1.23
seconds.
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EXAMPLE 3
At sea level, how long would
a pendulum be if it has a frequency of 2
Hz?
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SOLUTION 3
6.21 cm
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EXAMPLE 4
The Sears Building in Chicago sways
back and forth at a frequency of 0.1 Hz.
What is the period of its vibration?
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EXAMPLE 4
The period is 1/frequency.
= 1 vib / 0.1 Hz = 1 vib/0.1vib/sec =
10 sec.
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TYPES OF WAVES
• Transverse Wave
• Longitudinal Wave
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Longitudinal Wave
wave particles vibrate back
and forth along the path that
the wave travels.
Compressional Wave
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Transverse waves
wave particles vibrate
in an up-and-down motion.
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Longitudinal Wave
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Transverse Wave
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=14.0
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Wave Speed
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Wave Speed
Speed = Wavelength • Frequency
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Example 5
4. A ruby-throated hummingbird beats its
wings at a rate of about 70 wing beats
per second.
a. What is the frequency in Hertz of the
sound wave?
b. b. Assuming the sound wave moves
with a velocity of 350 m/s, what is the
wavelength of the wave?
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Solution 5:
f = 70 Hz and
wavelength = 5.0 m
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Example 6
Ocean waves are observed to travel along the
water surface during a developing storm. A
Coast Guard weather station observes that
there is a vertical distance from high point to
low point of 4.6 meters and a horizontal
distance of 8.6 meters between adjacent
crests. The waves splash into the station once
every 6.2 seconds. Determine the frequency
and the speed of these waves.
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Solution 6
The wavelength is 8.6 meters and the
period is 6.2 seconds.
The frequency can be determined from
the period. If T = 6.2 s, then
f =1 /T = 1 / (6.2 s)
f = 0.161 Hz
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Solution 6 Cont’d
Now find speed using the
v = f • wavelength equation.
v = f • wavelength =
(0.161 Hz) • (8.6 m)
v = 1.4 m/s
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Example 7
Two boats are anchored 4 meters apart. They
bob up and down, returning to the same up
position every 3 seconds. When one is up the
other is down. There are never any wave
crests between the boats. Calculate the speed
of the waves.
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Solution 7
The wavelength must be 8 meters
The period is 3 seconds so the frequency is 1 / T or
0.333 Hz.
Now use speed = f • wavelength
Substituting and solving for v, you will get
2.67 m/s.
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Wave Interference
Constructive
And
Destructive
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Constructive
Wave Interference
When the crest of one wave passes through,
or is superpositioned upon, the crest of
another wave, we say that the waves
constructively interfere.
Constructive interference also occurs when
the trough of one wave is superpositioned
upon the trough of another wave.
http://id.mind.net/~zona/mstm/physics/waves/interference/constructiveInterference/InterferenceExplanation2.html
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Destructive
Wave Interference
• When the crest of one wave passes
through, or is superpositioned upon, the
trough of another wave, we say that the
waves destructively interfere.
• During destructive interference, since the
positive amplitudes from one crest are
added to the negative amplitudes from the
other trough, this addition can look like a
subtraction.
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Doppler Effect
Some Examples
http://www.wfu.edu/physics/demolabs/demos/3/3b/3B40xx.html
http://www.walter-fendt.de/ph11e/dopplereff.htm
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Doppler Effect
When a source of waves and an observer of
waves are getting closer together, the
observer of the waves “sees” a frequency
for the waves that is higher than the
emitted frequency.
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Conventional Radar
All weather radars send out radio waves from an antenna. Objects in
the air, such as raindrops, snow crystals, hailstones or even insects
and dust, scatter or reflect some of the radio waves back to the
antenna. All weather radars, including Doppler, electronically convert
the reflected radio waves into pictures showing the location and
intensity of precipitation.
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Doppler Radar
Doppler radars also measure the frequency
change in returning radio waves.
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Doppler
Effect
Wave
Barrier
Wave
Barrier (2D)
Shock (3D)
Wave
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