Vibrations & Vibrations & WavesWaves

Unit 9Unit 9

All around us we see things All around us we see things that wiggle and jiggle. A that wiggle and jiggle. A

wiggle in time is a wiggle in time is a vibration. A vibration vibration. A vibration

cannot exist in one instant, cannot exist in one instant, but needs time to move but needs time to move

back and forth. A wiggle in back and forth. A wiggle in space and time is a wave. A space and time is a wave. A

wave cannot exist in one wave cannot exist in one place but must extend from place but must extend from

one place to another.one place to another.

Galileo discovered that the Galileo discovered that the time a pendulum takes to time a pendulum takes to

swing back and forth swing back and forth through small angles does through small angles does not depend on the mass of not depend on the mass of

the pendulum or on the the pendulum or on the distance through which it distance through which it swings. The time of a back swings. The time of a back and forth swing- called a and forth swing- called a

period- depends only on the period- depends only on the length of the pendulum and length of the pendulum and the acceleration of gravity.the acceleration of gravity.

DefinitionsDefinitions

Simple harmonic motion: the back and Simple harmonic motion: the back and forth vibratory motion of a swinging forth vibratory motion of a swinging pendulumpendulum

Sine curve: pictorial representation of a Sine curve: pictorial representation of a wavewave

Crest: high point of waveCrest: high point of wave Trough: low point of waveTrough: low point of wave Amplitude: distance from the mid-point to Amplitude: distance from the mid-point to

the crest (or trough) of the wavethe crest (or trough) of the wave Frequency: how often a vibration occursFrequency: how often a vibration occurs

The source of all waves is The source of all waves is something that vibrates. The something that vibrates. The

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

vibrating object is known, the vibrating object is known, the period can be calculated.period can be calculated.

Frequency= ___1____Frequency= ___1____ period period

The unit of frequency is the The unit of frequency is the HertzHertz

The unit of period is the The unit of period is the second.second.

Most of the information Most of the information around us gets to us in some around us gets to us in some

form of wave. Sound is energy form of wave. Sound is energy that travels to our ears in the that travels to our ears in the

form of one kind of wave. Light form of one kind of wave. Light is energy that comes to our is energy that comes to our

eyes in the form of a different eyes in the form of a different kind of wave (an kind of wave (an

electromagnetic wave). The electromagnetic wave). The signals that reach our radio signals that reach our radio

and television sets also travel and television sets also travel in the form of electromagnetic in the form of electromagnetic

waves.waves.

When energy is transferred by a wave When energy is transferred by a wave from vibrating source to a distant from vibrating source to a distant

receiver, there is no transfer of matter receiver, there is no transfer of matter between the two points. between the two points.

When a string is shaken up and down, a When a string is shaken up and down, a disturbance moves along the length of disturbance moves along the length of

the string. The string itself is not the string. The string itself is not moving. moving.

Drop a stone in a pond and you’ll Drop a stone in a pond and you’ll produce a wave that moves out from the produce a wave that moves out from the center in an expanding circle. It is the center in an expanding circle. It is the disturbance that moves, not the water, disturbance that moves, not the water, for after the disturbance passes, the for after the disturbance passes, the water is where it was before the wave water is where it was before the wave

passed.passed.

The speed of a wave The speed of a wave depends on the medium depends on the medium through which the wave through which the wave moves. Sound waves, for moves. Sound waves, for

example, move at speeds of example, move at speeds of about 340m/s in air about 340m/s in air

(depending on (depending on temperature), and about temperature), and about

four times faster in water. four times faster in water. Whatever the medium, the Whatever the medium, the

speed, wavelength, and speed, wavelength, and frequency of the wave are frequency of the wave are

related.related.

Wave speed= wavelength x Wave speed= wavelength x frequencyfrequency

Types of wavesTypes of waves

Transverse:Transverse:

The motion of the wave is The motion of the wave is at right angles to the at right angles to the direction in which the direction in which the wave is movingwave is moving

Waves in the stretched of Waves in the stretched of musical instruments and musical instruments and upon the surfaces of upon the surfaces of liquids are transverse, liquids are transverse, as well as the as well as the electromagnetic waves electromagnetic waves that make up radio that make up radio waves and light.waves and light.

Longitudinal:Longitudinal:

Particles of the medium Particles of the medium move along the move along the direction of the wavedirection of the wave

Sound waves are Sound waves are longitudinal waves.longitudinal waves.

More than one wave can More than one wave can exist at the same time in exist at the same time in the same space. If you the same space. If you

drop two rocks in water, drop two rocks in water, the waves produced by the waves produced by each can overlap and each can overlap and form an interference form an interference pattern. Within the pattern. Within the

pattern, waves may be pattern, waves may be increased, decreased, or increased, decreased, or

neutralized.neutralized.

When the crest of one wave When the crest of one wave overlaps the crest of another, their overlaps the crest of another, their

individual effects add together. individual effects add together. The result is a wave of increased The result is a wave of increased

amplitude. This is called amplitude. This is called constructive interference, or constructive interference, or

reinforcement.reinforcement.

When the crest of one wave When the crest of one wave overlaps the trough of another, overlaps the trough of another,

their individual effects are their individual effects are reduced. The high part of one reduced. The high part of one

wave simply fills in the low part of wave simply fills in the low part of another. This is called destructive another. This is called destructive

interference, or cancellation.interference, or cancellation.

Interference is characteristic of all Interference is characteristic of all wave motion.wave motion.

If you tie a rope to a wall and If you tie a rope to a wall and shake the free end up and shake the free end up and

down, you will produce a wave down, you will produce a wave in the rope. By shaking the in the rope. By shaking the

rope just right, you can cause rope just right, you can cause the original and reflected the original and reflected

waves to form a standing wave. waves to form a standing wave. In a standing wave certain In a standing wave certain

parts of the rope, called the parts of the rope, called the nodes, remain stationary. The nodes, remain stationary. The positions on a standing wave positions on a standing wave with the largest amplitudes with the largest amplitudes

are known as antinodes.are known as antinodes.

Standing waves are a Standing waves are a result of interference. result of interference.

When two waves of equal When two waves of equal amplitude and amplitude and

wavelength pass through wavelength pass through each other in opposite each other in opposite

directions, the waves are directions, the waves are always out of phase at always out of phase at

the nodes. The nodes are the nodes. The nodes are stable regions of stable regions of

destructive interference.destructive interference.

The apparent change in frequency due The apparent change in frequency due to the motion of the source (or receiver) to the motion of the source (or receiver)

is called the Doppler effect (after the is called the Doppler effect (after the Austrian scientist Christian Doppler, Austrian scientist Christian Doppler, 1803-1853). The greater the speed of 1803-1853). The greater the speed of

the source, the greater will be the the source, the greater will be the Doppler effect. The Doppler effect is Doppler effect. The Doppler effect is evident when you hear the changing evident when you hear the changing pitch of a car horn as the car passes pitch of a car horn as the car passes you. When the car approaches, the you. When the car approaches, the

pitch sounds higher than normal. This pitch sounds higher than normal. This occurs because the sound wave crests occurs because the sound wave crests are encountering you more frequently. are encountering you more frequently. When the car passes and moves away, When the car passes and moves away, you hear a drop in pitch because the you hear a drop in pitch because the

wave crests are encountering you less wave crests are encountering you less frequently.frequently.

Police make use of the Doppler Police make use of the Doppler effect of radar waves in measuring effect of radar waves in measuring the speeds of cars on the highway. the speeds of cars on the highway. Radar waves are electromagnetic Radar waves are electromagnetic waves, lower in frequency than waves, lower in frequency than

light and higher in frequency than light and higher in frequency than radio waves. Police bounce them radio waves. Police bounce them off moving cars, and a computer off moving cars, and a computer

built into the radar system built into the radar system calculates the speed of the car calculates the speed of the car

relative to the radar unit by relative to the radar unit by comparing the frequency of the comparing the frequency of the

radar emitted by the antenna with radar emitted by the antenna with the frequency of the reflected the frequency of the reflected

waves.waves.

The Doppler effect also occurs for The Doppler effect also occurs for light. When a light source light. When a light source

approaches, there is an increase in approaches, there is an increase in its measured frequency, and when its measured frequency, and when it recedes, there is a decrease in it recedes, there is a decrease in

its frequency. An increase in its frequency. An increase in frequency is called a blue shift, frequency is called a blue shift, because the increase is towards because the increase is towards

the high-frequency, or blue, end of the high-frequency, or blue, end of the color spectrum. A decrease in the color spectrum. A decrease in

frequency is called a red shift, frequency is called a red shift, referring to the low-frequency, or referring to the low-frequency, or

red, end of the color spectrum.red, end of the color spectrum.

When the speed of the source in a medium is When the speed of the source in a medium is as great as the speed of the waves it produces, as great as the speed of the waves it produces, something interesting happens. The waves pile something interesting happens. The waves pile up. The same thing happens when an aircraft up. The same thing happens when an aircraft travels at the speed of sound. The overlapping travels at the speed of sound. The overlapping

wave crests disrupt the flow of air over the wave crests disrupt the flow of air over the wings making it harder to control the plane wings making it harder to control the plane when it is flying close to the speed of sound. when it is flying close to the speed of sound. An airplane with sufficient power, however, An airplane with sufficient power, however,

can easily travel faster than the speed of can easily travel faster than the speed of sound. Then we say that it is supersonic- sound. Then we say that it is supersonic-

faster than sound. A supersonic airplane flies faster than sound. A supersonic airplane flies into smooth, undisturbed air because no into smooth, undisturbed air because no

sound wave can propagate out in front of it. It sound wave can propagate out in front of it. It outruns the waves it produces. The crests outruns the waves it produces. The crests

overlap at the edges and the pattern made by overlap at the edges and the pattern made by these overlapping crests is a V shape, called a these overlapping crests is a V shape, called a

bow wave, which appears to be dragging bow wave, which appears to be dragging behind.behind.

A speedboat knifing through the water A speedboat knifing through the water generates a two-dimensional bow wave. generates a two-dimensional bow wave.

A supersonic aircraft similarly A supersonic aircraft similarly generates a three-dimensional shock generates a three-dimensional shock wave. A shock wave is produced by wave. A shock wave is produced by

overlapping spheres that form a cone. overlapping spheres that form a cone. The conical shock wave generated by a The conical shock wave generated by a

supersonic craft spreads until it supersonic craft spreads until it reaches the ground. When the shell of reaches the ground. When the shell of compressed air that sweeps behind a compressed air that sweeps behind a supersonic craft reaches listeners on supersonic craft reaches listeners on

the ground below, the sharp crack they the ground below, the sharp crack they hear is described as a sonic boom. We hear is described as a sonic boom. We don’t hear a sonic boom from slower don’t hear a sonic boom from slower

than sound aircrafts because the sound than sound aircrafts because the sound wave crests reach our ears one at a wave crests reach our ears one at a

time.time.

A common misconception is A common misconception is that sonic booms are produced that sonic booms are produced at the moment an aircraft flies at the moment an aircraft flies through the “sound barrier.” through the “sound barrier.” The fact is that a shock wave The fact is that a shock wave and its resulting sonic boom and its resulting sonic boom

are swept continuously behind are swept continuously behind an aircraft traveling faster an aircraft traveling faster

than sound. The aircraft that than sound. The aircraft that generated this shock wave may generated this shock wave may have broken the sound barrier have broken the sound barrier

hours ago.hours ago.

FormulaFormula

Hooke’s Law: whenever a spring is Hooke’s Law: whenever a spring is stretched from its equilibrium position stretched from its equilibrium position and released, it will move back and and released, it will move back and forth on either side of the equilibrium forth on either side of the equilibrium position. The force that pulls it back and position. The force that pulls it back and attempts to restore the spring to attempts to restore the spring to equilibrium is called the restoring force.equilibrium is called the restoring force.

Restoring force (F)= force constant (k) x Restoring force (F)= force constant (k) x displacement from equilibrium (x)displacement from equilibrium (x)

F= kxF= kx

FormulaFormula

Period of a mass on a spring in simple Period of a mass on a spring in simple harmonic motion:harmonic motion:

Period= 2Period= 2ΠΠ √(m/k) √(m/k)

m= massm= mass

k= force constantk= force constant

A hummingbird beats its A hummingbird beats its wings up and down with wings up and down with

a frequency of 80 Hz. a frequency of 80 Hz. What is the period of the What is the period of the

hummingbird’s flaps?hummingbird’s flaps?

In anticipation of her first In anticipation of her first game, Alesia pulls back the game, Alesia pulls back the handle of a pinball machine handle of a pinball machine

a distance of 5cm. The a distance of 5cm. The force constant of the spring force constant of the spring

in the handle is 200N/m. in the handle is 200N/m. How much force must How much force must

Alesia exert?Alesia exert?

As Bianca stands on a bathroom As Bianca stands on a bathroom scale, whose force constant is scale, whose force constant is

220N/m, the needle on the scale 220N/m, the needle on the scale vibrates from side to side. vibrates from side to side.

If Bianca has a mass of 180kg, If Bianca has a mass of 180kg, what is the period of vibration of what is the period of vibration of the needle as it comes to rest?the needle as it comes to rest?

If Bianca goes on a diet, how will If Bianca goes on a diet, how will this change the period of this change the period of

vibration?vibration?

FormulaFormula

The period of a pendulum depends The period of a pendulum depends only upon the pendulum’s length.only upon the pendulum’s length.

Period= 2Period= 2ΠΠ √(L/g) √(L/g)

L= lengthL= length

g= acceleration due to gravityg= acceleration due to gravity

A tall, thin tree sways A tall, thin tree sways back and forth in the back and forth in the

breeze with a frequency breeze with a frequency of 2 Hz. What is the of 2 Hz. What is the period of the tree?period of the tree?

World-reknowned World-reknowned hypnotist Paulbar the hypnotist Paulbar the

Great swings his watch Great swings his watch from a 20cm chain in from a 20cm chain in

front of a subject’s eyes. front of a subject’s eyes. What is the period of the What is the period of the

swing of the watch?swing of the watch?

A spider swings in the A spider swings in the breeze from a silk thread breeze from a silk thread

with a period of 0.6s. with a period of 0.6s. How long is the spider’s How long is the spider’s

strand of silk?strand of silk?