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Vibrations of a Pendulum
Wave Description
Wave Speed
Transverse Waves
Longitudinal Waves
Wave Interference
Standing Waves
Doppler Effect
Bow Waves
Shock Waves
Good Vibrations
• A vibration is a periodic wiggle in time.
• A periodic wiggle in both space and time is
a wave. A wave extends from one place to
another. Examples are:
– light, which is an electromagnetic wave that
needs no medium.
– sound, which is a mechanical wave that needs
a medium.
Vibrations and Waves
Vibration
• Wiggle in time
Wave
• Wiggle in
space and time
Vibrations of a Pendulum
• If we suspend a stone at the end of a piece of
string, we have a simple pendulum.
• The pendulum swings to and fro at a rate that
– depends only on the length of the pendulum.
– does not depend upon the mass (just as mass does
not affect the rate at which a ball falls to the ground).
Vibrations of a Pendulum
• The time of one to-and-fro swing is called the
period.
• The longer the length of a pendulum, the
longer the period (just as the higher you drop a
ball from, the longer it takes to reach the
ground).
Vibrations of a Pendulum
A 1-meter-long pendulum has a bob with a mass
of 1 kg. Suppose that the bob is now replaced
with a different bob of mass 2 kg, how will the
period of the pendulum change?
A.
B.
C.
D.
It will double.
It will halve.
It will remain the same.
There is not enough information.
Vibrations of a Pendulum
A 1-meter-long pendulum has a bob with a mass of 1 kg.
Suppose that the bob is now replaced with a different bob
of mass 2 kg, how will the period of the pendulum change?
A.
B.
C.
D.
It will double.
It will halve.
It will remain the same.
There is not enough
information.
Explanation:
The period of a pendulum depends only on the length of
the pendulum, not on the mass. So changing the mass
will not change the period of the pendulum.
Vibrations of a Pendulum
A 1-meter-long pendulum has a bob with a mass
of 1 kg. Suppose that the bob is now tied to a
different string so that the length of the pendulum
is now 2 m. How will the period of the pendulum
change?
A.
B.
C.
D.
It will increase.
It will decrease.
It will remain the same.
There is not enough information.
Vibrations of a Pendulum
A 1-meter-long pendulum has a bob with a mass of 1 kg.
Suppose that the bob is now tied to a different string so that
the length of the pendulum is now 2 m. How will the period
of the pendulum change?
A.
B.
C.
D.
It will increase.
It will decrease.
It will remain the same.
There is not enough
information.
Explanation:
The period of a pendulum
increases with the length of
the pendulum.
Wave Description
• A wave is pictorially represented by a sine curve.
• A sine curve is obtained when
you trace out the path of a
vibrating pendulum over time.
– Put some sand in the
pendulum and let it swing.
– The sand drops through a hole
in the pendulum onto a sheet
of paper.
– As the pendulum swings back
and forth, pull the sheet of
paper on which the sand falls.
– The sand makes a sine curve
on the paper.
Wave Description
When a bob vibrates up and down, a
marking pen traces out a sine curve on the
paper that moves horizontally at constant
speed.
Wave Description
Vibration and wave characteristics
• Crests
– high points of the wave
• Troughs
– low points of the wave
Wave Description
Vibration and wave characteristics (continued)
• Amplitude
– distance from the midpoint to the crest or to the
trough
• Wavelength
– distance from the top of one crest to the top of the
next crest, or distance between successive identical
parts of the wave
Wave Description
How frequently a vibration occurs is called the
frequency.
• The unit for frequency is Hertz (Hz), after Heinrich Hertz
• A frequency of 1 Hz is a vibration that occurs once each
second.
• Mechanical objects (e.g., pendulums) have frequencies of
a few Hz.
• Sound has a frequency of a few 100 or 1000 Hz.
• Radio waves have frequencies of a few million Hz (MHz).
• Cell phones operate at few billon Hz (GHz).
Wave Description
Frequency
• Specifies the number of to and fro
vibrations in a given time
• Number of waves passing any point per
second
Example: 2 vibrations occurring in 1 second is a
frequency of 2 vibrations per second.
Wave Description
Period
• Time to complete one vibration
Period =
or, vice versa,
1
frequency
Frequency =
1
period
Example: Pendulum makes 2 vibrations in 1
second. Frequency is 2 Hz. Period of
vibration is 1⁄2 second.
Wave Description
A sound wave has a frequency of 500 Hz. What is
the period of vibration of the air molecules due to
the sound wave?
A.
B.
C.
D.
1s
0.01 s
0.002 s
0.005 s
Wave Description
A sound wave has a frequency of 500 Hz. What is
the period of vibration of the air molecules due to
the sound wave?
A.
B.
C.
D.
1s
0.01 s
0.002 s
0.005 s
Explanation:
Period =
1
frequency
So:
Period =
1
500 Hz
= 0.002 s
Wave Description
If the frequency of a particular wave is 20 Hz, its
period is
A. 1/20 second.
B. 20 seconds.
C. more than 20 seconds.
D. None of the above.
Wave Description
If the frequency of a particular wave is 20 Hz, its
period is
A.
B.
C.
D.
1/
second.
20 seconds.
more than 20 seconds.
None of the above.
20
Explanation:
Note when  = 20 Hz, T = 1/ = 1/(20 Hz) = 1/20
second.
Wave Motion
Wave motion
• Waves transport energy and not matter.
Example:
• Drop a stone in a quiet pond and the resulting ripples
carry no water across the pond.
• Waves travel across grass on a windy day.
• Molecules in air propagate a disturbance through air.
Wave Motion
Wave speed
• Describes how fast a disturbance moves through
a medium
• Related to frequency and wavelength of a wave
Wave speed = frequency  wavelength
Example:
• A wave with wavelength 1 meter and frequency of
1 Hz has a speed of 1 m/s.
Wave Speed
A wave with wavelength 10 meters and time
between crests of 0.5 second is traveling in water.
What is the wave speed?
A.
B.
C.
D.
0.1 m/s
2 m/s
5 m/s
20 m/s
Wave Speed
A wave with wavelength 10 meters and time between
crests of 0.5 second is traveling in water. What is the wave
speed?
A.
B.
C.
D.
0.1 m/s
2 m/s
5 m/s
20 m/s
Explanation:
So:
Frequency =
Frequency =
1
period
1
0.5 s
= 2 Hz
Also: Wave speed = frequency  wavelength
So:
Wave speed = 2 Hz  10 m = 20 m/s
Transverse and Longitudinal
Waves
Two common types of waves that differ because of
the direction in which the medium vibrates
compared with the direction of travel:
• longitudinal wave
• transverse wave
Transverse Waves
Transverse wave
• Medium vibrates perpendicularly to direction of
energy transfer
• Side-to-side movement
Example:

Vibrations in stretched strings of musical instruments
Light waves
S-waves that travel in the ground (providing geologic
information)
Transverse Waves
The distance between adjacent peaks in the direction of
travel for a transverse wave is its
A.
B.
C.
D.
frequency.
period.
wavelength.
amplitude.
Transverse Waves
The distance between adjacent peaks in the direction of
travel for a transverse wave is its
A.
B.
C.
D.
frequency.
period.
wavelength.
amplitude.
Explanation:
The wavelength of a transverse wave is also the
distance between adjacent troughs, or between any
adjacent identical parts of the waveform.
Transverse Waves
The vibrations along a transverse wave move in a direction
A.
B.
C.
D.
along the wave.
perpendicular to the wave.
Both A and B.
Neither A nor B.
Transverse Waves
The vibrations along a transverse wave move in a direction
A.
B.
C.
D.
along the wave.
perpendicular to the wave.
Both A and B.
Neither A nor B.
Comment:
The vibrations in a longitudinal wave, in contrast, are
along (or parallel to) the direction of wave travel.
Longitudinal Waves
Longitudinal wave
• Medium vibrates parallel to direction of energy
transfer
• Backward and forward movement
consists of
– compressions (wave compressed)
– rarefactions (stretched region between compressions)
Example: sound waves in solid, liquid, gas
Longitudinal Waves
Longitudinal wave
Example:
• sound waves in solid, liquid, gas
• P-waves that travel in the ground (providing geologic
information)
Longitudinal Waves
The wavelength of a longitudinal wave is the distance
between
A.
B.
C.
D.
successive compressions.
successive rarefactions.
Both A and B.
None of the above.
Longitudinal Waves
The wavelength of a longitudinal wave is the distance
between
A.
B.
C.
D.
successive compressions.
successive rarefactions.
Both A and B.
None of the above.
Wave Interference
• Wave interference occurs when two or more
waves interact with each other because they
occur in the same place at the same time.
• Superposition principle: The displacement
due the interference of waves is determined
by adding the disturbances produced by each
wave.
Wave Interference
Constructive interference :
When the crest of one wave
overlaps the crest of another,
together to produce a wave of
increased amplitude.
Destructive interference:
When the crest of one wave
overlaps the trough of
another, the high part of one
wave simply fills in the low
part of another. So, their
individual effects are reduced
(or even canceled out).
Wave Interference
Example:
• We see the interference pattern made when two vibrating
objects touch the surface of water.
• The regions where a crest of one wave overlaps the
trough of another to produce regions of zero amplitude.
• At points along these regions, the waves arrive out of
step, i.e., out of phase with each other.
Standing Waves
• If we tie a rope to a
wall and shake the free
end up and down, we
produce a train of
waves in the rope.
• The wall is too rigid to
shake, so the waves
are reflected back
along the rope.
• By shaking the rope
just right, we can
cause the incident and
reflected waves to form
a standing wave.
Standing Waves
• Nodes are the regions
of minimal or zero
displacement, with
minimal or zero
energy.
• Antinodes are the
regions of maximum
displacement and
maximum energy.
• Antinodes and nodes
occur equally apart
from each other.
Standing Waves
• Tie a tube to a firm support.
Shake the tube from side to
• If you shake the tube with the
right frequency, you will set up
a standing wave.
• If you shake the tube with
twice the frequency, a
standing wave of half the
wavelength, having two loops
results.
• If you shake the tube with
three times the frequency, a
standing wave of one-third
the wavelength, having three
loops results.
Standing Waves
• Examples:
– Waves in a guitar
string
– Sound waves
in a trumpet
Doppler Effect
The Doppler effect also applies to light.
• Increase in light frequency when light source
approaches you
• Decrease in light frequency when light source
moves away from you
• Star’s spin speed can be determined by shift
measurement
Doppler Effect
Doppler effect of light
– Blue shift
• increase in light frequency toward the blue end of the
spectrum
– Red shift
• decrease in light frequency toward the red end of the
spectrum
Example: Rapidly spinning star shows a red shift on
the side facing away from us and a blue shift on the
side facing us.
The Doppler Effect
The Doppler effect occurs for
A.
B.
C.
D.
sound.
light.
Both A and B.
Neither A nor B.
The Doppler Effect
The Doppler effect occurs for
A.
B.
C.
D.
sound.
light.
Both A and B.
Neither A nor B.
Explanation:
The Doppler effect occurs for both sound and light.
Astronomers measure the spin rates of stars by the
Doppler effect.
Bow Waves
Wave barrier
• Waves superimpose directly on top of one
another producing a “wall”.
Example: bug swimming as fast as the wave it makes
Bow Waves
Supersonic
• Aircraft flying faster than the speed of sound.
Bow wave
• V-shape form of overlapping waves when object travels
faster than wave speed.
• An increase in speed will produce a narrower V-shape
of overlapping waves.
Shock Waves
Shock wave
• Pattern of overlapping spheres that form a cone from
objects traveling faster than the speed of sound.
Shock Waves
Shock wave (continued)
• Consists of two cones.
– a high-pressure cone generated at
the bow of the supersonic aircraft
– a low-pressure cone that follows
toward (or at) the tail of the aircraft
• It is not required that a moving
source be noisy.
Shock Waves
Sonic boom
• Sharp cracking sound generated by a supersonic aircraft
• Intensity due to overpressure and underpressure of
atmospheric pressure between the two cones of the
shock waves
• Produced before it broke the
sound barrier
Example:
• supersonic bullet
• crack of circus whip
In attachment you can see the chapter 19 outline ppt,