Physics Study Notes
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Lesson 22 Vibrations and Waves
Introduction
a.
Vibration: A wiggle in time is a vibration. A vibration cannot exist in one instant, but needs time
to move back and forth.
b.
Wave: A wiggle in space and time is a wave. A wave cannot exist in one place, but must extend
from one place to another.
c.
Light and sound: are both forms of energy that move through space as waves.
Vibration of a Pendulum
a.
Period: The time of a back-and-forth pendulum swing depends only on the length of the
pendulum and the acceleration of the gravity. It does not depend on the mass of the pendulum
and the distance through which it swings.
b.
The period (T) of a simple pendulum is T = 2π (L/g)1/2, where L is the length of the pendulum,
and g is the acceleration of gravity.
c.
This is the reason why long-legged animals such as giraffes, horses, and ostriches, which run with
a slower gait than do short-legged animals such as hamsters and mice.
Wave Description
a.
Simple harmonic motion:
i)
The back-and-forth vibratory motion (called oscillatory motion) of a swing pendulum is
called simple harmonic motion.
ii) The criterion for Simple harmonic motion is that the restoring force is proportional to the
displacement from equilibrium.
1) The component of weight that restores a displaced pendulum to its equilibrium position is
directly proportional to the pendulum’s displacement (for small angle).
2) For a weight attached to a spring, based on the Hooke’s law: F= k∆x , where the force
that stretches (or compresses) a spring is directly proportional to the distance the spring is
stretched (or compressed).
3) For a person falls into a channel connecting the North pole and the South pole, the backand-forth motion is also a simple harmonic motion.
iii) The motion trace over time is actually a sine curve. A sine curve is pictorial representation of
a wave.
b.
Crest and trough: The high points of a wave are called crests, and the low points of a wave are
called troughs.
c.
Amplitude: The straight dashed line represents the “home” position, or midpoint of the vibration.
The term amplitude refers to the distance from the mid-point to the crest (or trough) of the wave.
So the amplitude equals the maximum displacement from equilibrium.
d.
Wavelength: The distance between successive identical parts of the wave such as from the top of
one crest to the top of the next one.
Wavelength
Period
Amplitude
Time
Crest
Amplitude
Distance
Trough
Mr. Lin
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Physics Study Notes
Lesson 22 Vibrations and Waves
e.
Frequency: The frequency of a vibration specifies the number of back-and-forth vibrations it
makes in a given time. A complete back-and-forth vibration is one cycle. The unit of frequency is
called hertz (Hz). One Hz is one cycle or vibration per second.
f.
Frequency unit:
i)
1 kilohertz (kHz— thousands of hertz) = 1 x 103 Hz
ii) 1 megahertz (MHz— millions of hertz) = 1 x 106 Hz
iii) 1 gigahertz (GHz— billions of hertz) = 1 x 109 Hz
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g.
AM radio is in kHz. FM radio is in MHz.
h.
frequency = 1/period and period = 1/frequency or f = 1/T and T = 1/f.
Wave Motion
a.
Most of the information around us gets to us in some form of wave, such as sound and light.
b.
When energy is transferred by a wave from a vibrating source to a distant receiver, there is no
transfer of matter between the two points. It is the disturbance that moves along the length of the
medium, not part of the medium itself.
Wave Speed
a.
The speed of a wave depends on the medium through which the wave moves.
b.
Sound wave moves at speeds of about 330 m/s to 350 m/s in air (depending on temperature), and
about four times faster in water.
c.
wave speed = wavelength x frequency = wavelength / period or
v = λ f = λ /T
where v is the wave speed
where λ is the wavelength
where f is the wave frequency
where T is the wave period
This relationship holds for all kinds of waves.
d.
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Transverse Waves
a.
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Whenever the motion of the medium is at right angles to the direction in which a wave travels, the
wave is a transverse wave.
Longitudinal Waves
a.
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The long wavelengths have low frequencies; the shorter wavelengths have higher frequencies.
Wavelength and frequency vary inversely to produce the same speed for all sounds.
Whenever the particles of the medium moves back-and-forth along the direction of the wave
rather than at right angles to it. This kind of wave is a longitudinal wave.
Interference
a.
A material object will not share its space with another object. But more than one vibration or wave
can exist at the same time in the same space.
b.
Two waves overlap each other will form an interference pattern. Within the pattern, wave effects
may be increased, decreased or neutralized.
c.
Constructive interference: When the crest of one wave overlaps with the crest of another, their
individual effects add together. The result is a wave of increased amplitude. This is called
constructive interference.
Mr. Lin
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Physics Study Notes
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Lesson 22 Vibrations and Waves
d.
Destructive interference: When the crest of one wave overlaps with the trough of another, their
individual effects are reduced. The high part of one wave simply fills in the low part of another.
This is called destructive interference or cancellation.
e.
The water wave interference pattern creates the gray “spokes” region where the crests of one wave
overlap the troughs of another to produce the region of zero amplitude. They are out of phase with
one another. The dark- and light-striped regions are where the crests of one wave overlap the
crests of another, and the troughs overlap as well. They are in phase with each other.
Standing Waves
a.
The incident (original) wave and reflected wave interfere to form a standing wave. In a standing
wave certain parts of the medium, called the nodes, remain stationary.
b.
The positions on a standing wave with the largest amplitudes are known as antinodes. Antinodes
occur halfway between nodes.
c.
Standing waves are the result of interference. When two waves of equal amplitude and
wavelength pass through each other in opposite direction, the wave are always out of phase at the
nodes. The nodes are stable regions of destructive interference.
d.
A variety of standing waves can be produced by increasing the frequency of vibration. Starting up
with a standing wave of one segment (1/2 wavelength). Then increase the frequency to 2 times,
and get a standing wave of two segments (1 wavelength). Then increase the frequency to 3 times,
and get a standing wave of three segments (3/2 wavelength).
e.
Standing waves can be produced in either transverse or longitudinal waves.
The Doppler Effect
a.
When a wave source create water ripple at a fixed position and at constant frequency, the crest of
the wave it makes are concentric circles and the distance between wave crests (wavelength) will
be the same for all successive waves because the wave speed is the same in all directions. The
frequency of wave motion at point A and B are the same.
A
B
A
B
b.
If the wave source moves across the water at a speed less than the water speed, the wave pattern is
distorted and is no longer concentric. The centers of the circular crests move in the direction of the
moving wave source. Although the wave source still create water ripple at the same frequency, the
wave motion at point B would be at higher frequency. This is because each successive crest has a
shorter distance to travel so they arrive at B more frequently. At the point A, the wave motion is at
lower frequency because longer time between wave crests arrivals.
c.
This change in frequency due to the motion of the source (or receiver) is called the Doppler
effect. The greater speed of the source, the greater will be the Doppler effect.
d.
Water wave travels over the flat surface of the water. Sound and light waves travel in threedimensional space in all direction like an expanding balloon. The Doppler effect is also applicable
in sound and light waves.
e.
The Doppler effect is evident when you hear the changing pitch of a car horn as the car pass you.
When the car approaches, the pitch sounds higher than normal. When the car passes and moves
away, you hear a drop in pitch.
f.
Police make use of the Doppler effect of radar waves in measuring the speed of cars on the
highway.
Mr. Lin
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Physics Study Notes
Lesson 22 Vibrations and Waves
g.
When a light source approaches, there is an increase in its measured frequency (a blue shift), and
when it recedes, there is a decrease in its frequency (a red shift). A measurement of this shift
enables astronomers to calculate their speeds of approaching or recession.
h.
The Doppler effect is about the change of the perceived frequency of the wave, not the change of
wave speed.
10 Bow Waves
a.
When the speed of the source in a medium is as great as the speed of the waves it produces, the
waves pile up. They superimpose on one another directly in front of the source. The source moves
right in front of the waves it producing.
b.
The same thing happens when an aircraft travels at the speed of sound. The overlapping wave
crests disrupt the flow of air over the wings, so that it is harder to control the plane when it is
flying close to the speed of sound. Just as boat can easily travel faster than the speed of water, an
airplane can become supersonic with sufficient power. A supersonic plane flies into smooth and
undisturbed air because no sound wave can propagate out in front of it.
c.
When the source moves faster than the wave speed, the overlapping crests create a V shape, called
a bow wave. The greater the moving speed produces a narrower V shape.
v less than wave speed
v equal to wave speed
v larger than wave speed
11 Shock Waves
a.
A speedboat knifing through the water generates a 2-D bow wave. A supersonic aircraft generates
a 3-D shock wave. The conical shell of compressed air that sweeps behinds a supersonic aircraft
reaches listeners on the ground below, the sharp crack they hear is called a sonic boom. The highpressure sound due to the overlapping crests has much the same effect as an explosion.
The conical shell reaches the ground
b.
It is not necessary that the moving source emit sound for it to produce a shock wave. A supersonic
object will make sound.
c.
The loud sound will hurt your ears just as the bright light will hurt your eyes.
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