# Ch. 19 Vibrations and Waves

a periodic wiggle in time

a complete to-and-fro oscillation is one vibration

Vibration
a periodic wiggle in both space and time
extends from one place to another
the source of all waves is something that is vibrating
mechanical waves require a medium
Wave
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Sound is a mechanical wave, the propagation of vibrations through a material medium – a solid, liquid, or gas. If there is no material medium to vibrate, then no sound is possible. Sound cannot travel in a vacuum.
Light and sound are both vibrations that propagate through space as waves but two very different kinds of waves
a pictorial representation of a wave produced by simple harmonic motion.

as for a water wave, the high points of a sine wave are called crests and the low points are called troughs.

midpoint of the vibration is the equilibrium position (dashed line).

Sine curve
the time of a to-and-fro swing, called the period, does not depend on either the mass of the pendulum or the size of the arc through which it swings.

in addition to length, the period of a pendulum depends on the acceleration due to gravity

the pendulum with the greatest frequency is the pendulum with the shortest length (period)

Galileo discovered that the time a pendulum takes to swing to and fro through small distances depends on only the length of the pendulum.
in all cases, the motions are independent of mass.
If you drop two balls of different mass, they accelerate at g. Let them slide without friction down the incline, and they slide together at the same fraction of g. Tie them to strings of the same length so that they are pendulums, and they swing to and fro in unison.
the distance from the midpoint to the crest (or trough) of the wave. so the amplitude equals the maximum displacement from equilibrium.
amplitude
the distance from the top of one crest to the top of the next crest.
wavelength
how frequently a vibration occurs (the number of to-and-fro vibrations it makes in a given time)

the frequency of the vibrating source and the frequency of the wave it produces are the same.

radio-wave frequencies are the freq at which electrons are forced to vibrate in the antenna of a radio stations transmitting tower.

the freq of a pendulum depends on the restoring force, which is gravity. similarly, mass doesn’t affect free fall acceleration.

frequency
the period of a vibration or wave is the time for one complete vibration

shortest period causes shortest length

period and freq is independent of mass.

period
freq = 1/period

period = 1/freq

if an objects frequency is known then its period can be calculated.

What happens to the period of a wave when the freq decreases? the period increases

What happens to wavelength of a wave when freq decreases? (use wave speed eqn) wavelength increases.

Frequency (vibrations per second) and period (seconds per vibration) are reciprocals:
a. 90 cycles per s = 90 Hz
b. 1/90 s
An electric toothbrush completes 90 cycles every second. What are
a. its frequency
b. its period
named after Heinrich Hertz, who demonstrated radio waves in 1886. One vibration per second is 1 hertz (Hz)
1 unit of freq is called the hertz
a. 1/10 Hz
b. 10 s
Gusts of wind make the Willis tower in Chicago sway back and forth, completing a cycle in 10 s. What are
a. its frequency
b. its period
The medium returns to its initial condition after the disturbance has passed. What is propagated is the disturbance not the medium itself.
Through wave motion, energy can be transferred from a source to a receiver without the transfer of matter between the two points.
the motion of the medium is at right angles to the direction of the wave speed. The right-angled, or sideways, motion is called transverse motion.

because the motion of the medium is transverse tot he direction the wave travels, this type of wave is called a transverse wave.

Waves in the stretched strings of instruments are transverse. Radio waves and light waves are also transverse.

Slinky example: One end of the slinky is connected to a firm wall. Shaking the mobile end of the slinky from side to side in a direction perpendicular to the slinky produces a transverse wave.

Transverse waves
amplitude, frequency, wavelength, and speed.
Like a transverse wave, a longitudinal wave has
sound
Which of the following is not a transverse wave?
101,000,000 (101 million)
How many vibrations per second are associated with a 101-MHz radio wave?
Motion of the medium is along the direction of the wave rather than at right angles to it. Medium vibrates parallel to the direction of energy transfer.

Slinky example: created by rapidly pulling and pushing the mobile end of the slinky toward and away from you in a direction parallel to the slinky.

longitudinal waves typifies sound waves.

In between successive compressions is a stretched region called a rarefaction.

both compressions and rarefactions travel in the same direction along the slinky

wavelength of a longitudinal wave is the distance between successive compressions or equivalently the distance between successive rarefactions.

the most common example of longitudinal waves is sound in air
sound waves = pressure waves = long. waves

Longitudinal wave
it can’t travel in a vacuum because there’s nothing to compress and stretch
Sound requires a medium
wave speed = wavelength / period

since period is the inverse of frequency, the formula can also be written as:
wave speed = (wavelength) x (frequency)

holds true for ALL kinds of waves

Wave speed
30 m/s.

speed = distance / time.
x = (3 x 10m)/1s = 30 m/s

If a train of freight cars, each 10 m long, rolls by you at the rate of three cars each second, what is the speed of the train?
the freq of the wave is 3 Hz, its wavelength is 2 m, and its wave speed = freq x wavelength = 3 x 2 = 6 m/s
If a water wave oscillates up and down three times each second and the distance between wave crests is 2m, what is its freq? what is its wavelength? what is its wave speed?
if we drop two rocks in water, the waves produced by each can meet and produce wave interference. the overlapping of waves can form an interference pattern. Within the pattern, wave effects may be increased, decreased or neutralized.
more than one vibration or wave can exist at the same time in the same space
when more than one wave occupies the same space at the same time, the displacements add at every point
Superposition principle
when the crest of one wave overlaps the crest of another, their individual effects add together to produce a wave of increased amplitude
Constructive interference
When the crest of one wave overlaps the trough of another, their individual effects are reduced. the high part of one wave simply fills in the low part of another.
destructive interference
regions where a crest of one wave overlaps the trough of another to produce regions of zero amplitude. the waves arrive “out of step” or out of phase with one another
“out of phase”
Interference is characteristic of all wave motion
when two sets of waves of equal amplitude and wavelength pass through each other in opposite directions, the waves are steadily in and out of phase with each other.

this occurs for a wave that reflects upon itself. Stable regions of constructive and destructive interference are produced.

the incident (–>) and reflected (<--) waves interfere to produce a standing wave where the nodes of waves appear to be standing still. Nodes are at the regions of minimal or zero displacement, with minimal or zero energy. Antinodes, in contrast, are the regions of maximum displacement and maximum energy. antinodes occur halfway between nodes the distance between successive nodes is half wavelength; two loops constitute a full wavelength. can be produced with either transverse or longitudinal vibrations.

Standing wave
Yes. this is called destructive interference. In a standing wave in a rope, for example, parts of the rope have no amplitude – the nodes
Is it possible for one wave to cancel another wave so that no amplitude remains at certain points?
If you impart twice the freq to the rope, you’ll produce a standing wave with twice as many segments, so you’ll have six segments. since a full wavelength has two segments, you’ll have three complete wavelengths in your standing wave.
Suppose you set up a standing wave of three segments. If you shake with twice as much freq, how many wave segments will occur in your new standing wave? How many wavelengths?
wave speed is the same in all directions
concentric circles
change in freq due to the motion of the source (or receiver)

the shift in received freq due to the motion of a vibrating source toward or away from a receiver.

an appreciable Doppler effect does NOT occur when something is coming at right angles.

Doppler effect is evident when you hear the changing pitch of an ambulance siren as it passes you. when the vehicle approaches, the pitch is higher than normal. this is because the crests of the sound waves encounter your ear more freq. when the vehicle passes and moves away, you hear a drop in pitch because the crests of the waves hit your ear less freq.

Doppler effect for light: an increase in freq is called a blue shift b/c the increase is toward the high freq (or blue) end of the color spectrum. a decrease in freq is called a red shift, referring to a shift toward the lower freq (or red) end of the color spec.

Doppler Effect
neither! both the freq and the wavelength undergo a change when the source is moving, but the wave speed does not. be clear about the distinction between freq and speed.
while youre at rest, a sound source moves toward you. do you measure the speed of its sound wave to be greater or less than if the source were stationary
the waves pile up in front of the source
When the speed of a source is as great as the speed of the waves it produces (source moves at wave speed), something interesting occurs:
the pattern produced by a bug (source) swimming faster than the wave speed. the points at which adjacent waves overlap (X) produce the V shape.

outruns the waves it produces, waves appear to be dragging behind the source.

bow wave
the barrier is not real. what actually happens is that the overlapping wave crests disrupt the flow of air over the wings, making it more difficult to control the aircraft. an aircraft with sufficient power easily travels faster than the speed of sound. then we say it is supersonic. the aircraft may have exceeded the speed of sound earlier.
“break the sound barrier”
produced overlapping spheres that form a cone (much like the overlapping circles that form a V in a bow wave). the conical wave generated by a supersonic craft spreads until reaches the ground and as the shell of compressed air sweeps behind the aircraft, once it reaches the listeners on the ground below, the sharp crack they hear is described as a sonic boom.
shock wave
this is not so. the fact is that a shock wave and its resulting sonic boom are swept continuously behind and below an aircraft traveling faster than sound.
a common misconception is that sonic booms are produced when an aircraft flies through the “sound barrier”
Energy moves from source to receiver
In one word, what is it that moves from source to receiver in wave motion?
perpendicular to the direction of wave travel
In what direction are the vibrations relative to the direction of wave travel in a transverse wave?
to keep up with produced waves, it must swim at wave speed. to produce a bow wave, the bug must swim faster than wave speed
How fast must a bug swim to keep up with the waves it produces? How fast must it move to produce a bow wave?
The faster the source, the narrower the V shape
how does the V shape of a bow wave depend on the speed of the source
freq = 2 bobs/second = 2 Hz
period = 1/freq = 1/2 second
amplitude is the distance from the equilibrium position tot he maximum displacement: one half the 20 cm peak to peak distance, or 10 cm.
A weight suspended from a spring is seen to bob up and down over a distance of 20 cm twice each second. What is its freq? its period? its amplitude?
it increases, because period and freq are reciprocals of each other.
What happens to the period of a wave when the freq decreases?
for mechanical waves, the source is something that vibrates. for electromagnetic waves, the source is vibrating electric charge.
What is the source of mechanical waves? of electromagnetic wave?
because the speed of light is about a million times faster than the speed of sound.
Why is lightening seen before thunder is heard?
police use radar waves that are reflected from moving cars. from the shift in the returned freq, the speed of the reflectors (car bodies) is determined.
How does the doppler effect aid police in detecting speeding motorists?
Yes. a supersonic fish in water wold produce a shock wave and hence a sonic boom for the same reason it would if it were traveling faster than sound in air.
Imagine a superfast fish that is able to swim faster than the speed of sound in water. would such a fish produce a “sonic boom”?
wave speed involves the rate of travel while wave frequency involves how frequently vibration occurs.
wave speed vs wave freq

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