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Conceptual Physics
Study Notes & Questions: Vibrations (Chap. 14)
1)
A vibration is a back and forth motion (p289). Now, moving any mass
back and forth requires acceleration and a force to push or pull it.
Energy is needed to get a vibration started—work has to be done on
the mass.
2)
The fact that a system wants to vibrate means a restoring force is
also present. That is, work is done to move the mass from its
equilibrium state (giving it potential energy), then a restoring force
pulls it back toward its equilibrium state. In the case of pendulum-like
motion (which occurs in some form or another in almost all physical
systems), momentum and kinetic energy are built up by the restoring
force acting on the mass—causing the system to shoot past
equilibrium until an opposite-acting restoring force slows it down and
pulls it once again back toward equilibrium. Once a vibration starts in
a frictionless, elastic system, no energy is required to keep it
vibrating—it is like an ideal pendulum (p290)—with a constant
interchange between potential and kinetic energy.
3)
A system that exhibits simple harmonic motion (p290) means that the
time period of the vibration is constant, no matter what the initial size
of displacement is. For example, in an ideal clock pendulum, the time
period between its ticks will always be 1 second, no matter whether
the pendulum is swing back and forth by 1 inch, 2 inches or 7 inches.
4)
A vibration that travels is called a wave. (p291) Think of a water wave.
It moves with a certain velocity (v), (p292) that is, it has speed and
direction. The highest point of the wave is called its crest; the lowest
point is called its trough. The distance between two adjacent crests or
two adjacent troughs is called the wavelength (l). The time (in
seconds) it takes the wave (in a fixed spot) to change from crest to
trough to crest again, is called its period. How many times this cycle
occurs in one second is called the wave frequency (f), and its units
are hertz (Hz; 1/sec). The wave equation is: v = l f (p293). Wave
amplitude is the distance the wave crests and troughs extend from
equilibrium—so the total magnitude between the crest height and the
trough depth equals twice the wave amplitude.
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5)
A vibration holds energy. If the vibration occurs in an elastic or semielastic medium, the vibration propagates outward through medium,
carrying energy with it. Traveling waves carry energy. Almost all
waves need a medium in which to travel. The exception is light—light
waves do not need a medium—they sort of create their own (more later…)
6)
There are 2 types of waves:
a) In a semi-rigid medium—like a solid—back and forth vibrations
can ripple forward through the matrix of atoms or molecules
perpendicular to the back & forth motion. This is called a
transverse wave—the vibration spreads out transverse to the
direction of vibration. For example, the up & down wiggle of
one atom is transferred via intermolecular forces to its
neighboring atoms—this wiggling motion spreads left and right,
even though the actual atomic motion is up & down. Certain
types of seismic (earth) vibrations are transverse waves. Water
waves and other types of surface waves are also transverse
waves. Light is a transverse wave. Although transverse waves
can travel on the surface interface of a liquid, they can not travel
inside the liquid—the atoms are too loosely bound for the up &
down motion to be transferred right and left to neighboring
atoms via intermolecular attraction.
b) In a compressive or semi-compressive medium—which includes
all states of matter—longitudinal waves (compression waves)
can travel. In this case, the wave consists of local compression
and rarefaction (“thinning out”) that occur along the same
direction the wave is traveling. Sound is a longitudinal wave. So
are certain types of seismic waves.
7)
Waves superimpose on one another, that is their amplitudes combine
to make the composite wave larger (constructive interference) or
make the wave smaller (destructive interference). (p296)
8)
Light waves can interfere with one another, especially when they are
partially reflected off thin molecular membranes like soap bubbles or
oil slicks. This type of interference pattern is wavelength (that is,
color) dependent. What is iridescence? (p297)
9)
Standing waves are essentially physically extended vibrations (p298).
What are the nodes and anti-nodes of standing waves?
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10) The Doppler Effect occurs when a wave source is moving toward you
or away from you—OR you are moving toward or away from the wave
source. The waves reaching you (for example, sound waves coming
from an ambulance) are shifted up in frequency as the source
approaches, and they shift down in frequency as the source recedes
(p299). How does Doppler radar detect tornadoes? (p300)
11) In the spread pattern of a wave dispersion (e.g. waves spreading
across a pond) can be described by its wave fronts—that is—the
continuous lines of wave crests. Wave fronts are perpendicular to the
direction of wave travel.
12) In some circumstances, wave fronts pile up on top of one another,
creating a shock wave—which produces a very intense vibrational jolt
when it passes. What is an example of a shock wave (p301)?
13) Usually, waves interact only weakly with their host medium.
Resonance occurs when a passing wave’s frequency corresponds to
the natural vibrational frequency of its medium. In this case, the
medium’s vibrations can build up very large amplitude swings. What
can happen in cases of runaway resonant vibrations? (p303)
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