vibrations & waves 19 & 20 sound in a vacuum sound is the propagation of vibrations through...

VIBRATIONS & WAVES19 & 20

Sound in a Vacuum• Sound is the

propagation of vibrations through a material medium—a solid, liquid, or gas.

• If there is no medium to vibrate, then no sound is possible.

• Sound cannot travel in a vacuum.

Vibrations and Waves

• Oar in Water• Wings of a Bee• Electrons in an Light

Bulb

Water Waves Sound Waves Light Waves

“Wiggles in Time” “Wiggles in Space”

Vibrations and Waves

• Waves transmit energy and information.

• Sound and Light are both waves.

• Let them slide without friction down the same incline, and they slide together at the same fraction of g.

• Tie them to strings of the same length so they are pendulums, and they swing to and fro in unison.

• In all cases, the motions are independent of mass

If you drop two balls of different mass they accelerate at g.

Pendulums & Galileo• The period does not depend on the amount of

mass.

• The period does depend on the length of the pendulum.

T l g 2

Apr 19, 2023 Physics 1 (Garcia) SJSU

Period

Time required for a full oscillation (one round trip) is called the period of oscillation.

Pendulum that is about one meter long has a period of two seconds per oscillation.

Note: Measure the period of a pendulum in lab.


Frequency

Frequency is the inverse of the period,

(Frequency) =

For example, for a period of 2 seconds per oscillation, the frequency is ½ oscillation per second or ½ Hertz.

1 Hertz = 1 oscillation per second

(Period)

1

Amplitude

The distance from the rest position is the amplitude of oscillation.

Amplitude

• Amplitude• the distance from the midpoint to the

crest (or trough) of the wave. • So the amplitude equals the maximum

displacement from equilibrium.

Like a water wave, a sine wave has crests, troughs and amplitude

A sine curve is a pictorial representation of a wave.


Waves

Concept of vibrations extends into the phenomenon of wave motion.

Water waves

Light waves

Sound

Radio

String

WAVE DESCRIPTION

The to-and-fro vibratory motion (often called oscillatory motion) of a swinging pendulum in a small arc is called simple harmonic motion.

Wave Motion• medium - the stuff that carries the wave

Waves Mediumwater waves water

waves on a rope rope

stadium waves people

sound air

light space (vacuum)

water wave

• barring obstacles the surface of the water will have been disturbed, but the water itself will have gone nowhere.

• A leaf on the surface will bob up and down as the waves pass, but will end up where it started.

a stone dropped into a quiet pond has waves travel outward in expanding circles

Wave Motion

• 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

• The energy transferred from a vibrating source to a receiver is carried by a disturbance in a medium, not by matter moving from one place to another within the medium

Wave Speed...• the speed with which waves pass by a

particular point• e.g. the speed of a surfer

• It depends only on the type of medium.

• Wave Speed = Frequency Wavelength

Waves on a RopeTable in Notes – Appearance, Node, Antinodes, Wavelength, Frequency

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

• A station at 101.7 MHz FM -a frequency of 101,700,000 hertz.

• The source of all waves is something that vibrates.

Electrons in the transmitting antenna vibrate 940,000 times each second and produce 940-kHz radio waves.

Wave Motion

Wave Speed...• the speed with which waves pass by a

particular point• e.g. the speed of a surfer

• It depends only on the type of medium.

• Wave Speed = Frequency Wavelength

Waves on a RopeTable in Notes – Appearance, Node, Antinodes, Wavelength, Frequency

Wave Speed ProblemThe water waves below are traveling with a speed of 2 m/s and splashing periodically against the Wilbert's perch. Each adjacent crest is 4 meters apart and splashes Wilbert’s feet upon reaching his perch. How much time passes between each successive drenching?


Wave Motion

Transverse Waves

For transverse waves the wave’s amplitude is perpendicular to the wave’s motion.

Amplitude

Amplitude


Wavelength

Wavelength is distance between crests or between troughs of waves.

Longitudinal

Transverse

Transverse Waves• side to side vibration in a direction

perpendicular to the wave's motion

• Examples: – water waves– waves on a rope– string musical instruments

Transverse Waves

Longitudinal Waves• back and forth vibration in a

direction parallel to the wave's motion

• Examples: – slinky waves– sounds waves (vortex box)

Longitudinal Waves


Doing “The Wave”

Synchronized standing and sitting by a stadium’s crowd is an example of a transverse wave.

Video analysis indicates that it takes only a few dozen fans leaping to their feet with their arms up to trigger a wave. Once started, it usually rolls in a clockwise direction at a rate of about 40 feet per second, or about 20 seats per second. At any given time, the wave pulse is about 15 seats wide.

• Waves generated by an earthquake. P waves are longitudinal and travel through both molten and solid materials.

• S waves are transverse and travel only through solid materials.

• Reflections and refractions of the waves provide information about the Earth’s interior.


Longitudinal Waves

For longitudinal waves, amplitude and wave motion are parallel.

Wave Motion

Amplitude

Amplitude

A crowd can do a longitudinal wave by moving side-to-side instead of up-and-down

Transverse vs LongitudinalDemonstration


Wave Speed

The speed at which waves travel is called the wave speed.

Speed of sound = 330 m/s = 725 mi/hrSpeed of light = 300,000,000 m/s

Water waves at the beach move a few miles per hour

Tsunami Waves

Tsunamis are ordinary water waves, just like waves in your bathtub, but because they are typically generated by deep sea earthquakes they carry huge amounts of energy and momentum, traveling at almost 500 mph while in the deep ocean.


The tsunami of 26 December 26th 2004 was produced by an earthquake whose epicenter was located off the coast of Indonesia in the Indian Ocean. The death toll is estimated at over a quarter of a million persons.

Animation by Vasily V. Titov


Wave Relations

Wave speed, wavelength & frequency related.

(Wave speed) = (Wavelength) x (Frequency)

(Wave length) =

(Frequency) =

(Wave speed)

(Frequency)

(Wave speed)(Wavelength)

Ruben’s Flame Demo

If a water wave oscillated up and down three times each second and the distance between wave crest is 2 m, what is its frequency?

Answer: 3 HzWhat is its period?

Answer: 1/3 secondWhat is its wavelength?

Answer: 2 mWhat is its wave speed?

Answer: 6 m/s

Example Test Question:If you double the frequency of a vibrating object, what happens to the period?

a) the period doublesb) the period stays the samec) the period is cut in halfd) not enough information is given to answer this question.

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Example Question

Changing which of the following affects the period of a pendulum?– a) mass– b) amplitude– c) length– d) angle

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What is the frequency in vibrations per second of a 60-Hz wave?

Answer: 60 cycles per second

What is its period?Answer: 1/60 second


Demo: Hearing Sound

Range of human hearing is roughly 20 Hertz to 20,000 Hertz.

Wave speed for sound is 330 m/sWavelength of 20 Hertz is 16 m (about 50 ft)Wavelength of 20,000 Hz is 1.6 cm (½ inch)

Hearing in Animals

Frequency range varies widely, depending on natural adaptation using sound to communicate, locate food, avoid predators, etc.

Amplitude

Crest

Baseline

Trough

Wavelength

Transverse Wave

INTERFERENCE• Constructive or destructive interference

results when waves add.

• Standing Waves - wave pattern produced from interfering waves– Examples

• Vibrating Strings in Lab• Organ Pipe in Lab• Bell Wave Machine in Class

Interference• Interference Pattern – within a pattern, wave effects

may be increased, decreased, or neutralized• Constructive Interference (reinforcement) – the crest

of one wave overlaps the crest of another, their individual effects add together producing an increased amplitude

• Destructive Interference (cancellation) – the crest of one wave overlaps the trough of another, their individual effects are reduced

• When waves produce areas of zero amplitude, they are “out of phase”

• When the crest of one wave overlaps the crest of another, they are “in phase”

constructive interference.

• destructive 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.

when the crest of one wave overlaps the crest of another, their individual effects add together to produce a wave of increased amplitude.

2 ½ meters

20 cm

Wavelength = 1 m

Example Wave

Amplitude = 10 cm

Number of Nodes = 6

Noise-Canceling Headphones

Noise-canceling headphones use a microphone that listens for noise and a speaker that produces the same noise but out of phase (cancellation by destructive interference)

External Noise

Canceling Sound

Standing WavesWhen two sets of waves of equal amplitude and

wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is

“standing still.”

It is a changing interference pattern.

Today you will create such patterns on a vibrating string.

There is no vibration at a node.There is maximum vibration at an antinode. is twice the distance between successive nodes

or successive antinotes.

Parameters of a Standing WaveParameters of a Standing Wave


Standing Waves and Phase

Standing waves are another example of constructive and destructive interference.

Two sets of overlapping water waves produce an

interference pattern. The left image is an idealized drawing

of the expanding waves from the two sources. The right

image is a photograph of an actual interference pattern.

Interference is characteristic of all wave motion, whether the waves are water waves, sound waves, or light waves

Waves are out of phase with each other when the regions where a crest of one wave overlaps the trough of another to produce regions of zero amplitude and wave points along these regions arrive out of step.

Interference Animation


Doppler Effect

Sound coming from a moving object has a different wavelength and frequency than if it were stationary.

If moving towards you, wavelength shorter and frequency higher.

If moving away, wavelength longer and frequency lower.

DOPPLER EFFECT• the change in wavelength due to motion of

the source

• "Wheeeeeeeeeeee…….Oooooooooooooo”

• Examples:– moving cars and trains– moving buzzer in a nerf ball (in class)– rotating whistle

Draw Doppler Picture

Java Doppler Effect

http://www.physics.sfasu.edu/markworth/doppler.htm

http://www.physics.sfasu.edu/markworth/doppler.htm

The Doppler Effect• Doppler Effect – the apparent change in frequency due

to the motion of the source (or receiver)• Spherical sound or light wave crests ahead of a moving

source are closer together than those behind the source and encounter a receiver more frequently

• Blue Shift – an increase in frequency towards the high-frequency, or blue, end of the light spectrum (light source is moving towards receiver)

• Red Shift - a decrease in frequency towards the low-frequency, or red, end of the light spectrum (light source is moving away from the receiver)

• Distant galaxies show a red shift in the light they emit, indicating that the universe is expanding (or moving further apart)

The Doppler Effect

Blue Shift and Red Shift

• When a light source

approaches, there is

an increase in its

measured frequency

called a blue shift;

and, when it recedes,

there is a decrease in

its frequency called a

red shift spectrum

Bow Waves

• What actually happens is that the overlapping wave crests disrupt the flow of air over the wings, making it more difficult to control the craft. But the barrier is not real.

In the early days of jet aircraft, it was believed that a pile-up of sound waves in front of the airplane imposed a “sound barrier” and that, in order to go faster than the speed of sound, the plane would have to “break the sound barrier.”

Bow and Shock Waves

• Bow Wave – when the speed of the source in a medium is as great, or greater, than the speed of the wave it produces it will catch up to the wave crests and pass them producing a v-shape

• Shock Wave – like a bow wave, but in three dimensions, produces a cone-shape

• Sonic Boom – produced when the conical shell of compressed air that sweeps behind a supersonic jet reaches listeners on the ground below

Bow Wave

• Patterns produced by a bug swimming at successively greater speeds. Overlapping at the edges occurs only when the bug swims faster than wave speed.

after the speed of the source exceeds wave speed, increased speed of the source produces a narrower V shape

Sonic Booms• Only when the craft moves faster than

sound do the waves overlap to reach the listener in a single burst.

• The sudden increase in pressure is much the same in effect as the sudden expansion of air produced by an explosion.

• Both processes direct a burst of high-pressure air to the listener.

• The ear is hard pressed to distinguish between the high pressure from an explosion and the high pressure from many overlapping waves.

We don’t hear a sonic boom from slower-than-sound, or subsonic, aircraft because the sound waves reaching our ears are perceived as one continuous tone.

The mach cone and shock wavefronts are very noticeable

The speed of sound in the medium (vs = v, or Mach 1). The speed of sound in air at sea level is

about 340 m/s or about 750 mph.

The wavefronts in front of the source are now all bunched up at the same point. As a result, an

observer in front of the source will detect nothing until the source arrives. The pressure front

will be quite intense (a shock wave), due to all the wavefronts adding together, and will not be

percieved as a pitch but as a "thump" of sound as the pressure wall passes by.

The figure at right shows a bullet travelling at Mach 1.01. You can see the shock wave front just

ahead of the bullet. Jet pilots flying at Mach 1 report that there is a noticeable "wall" or

"barrier" which must be penetrated before achieving supersonic speeds. This "wall" is due to

the intense pressure front, and flying within this pressure front produces a very turbulent and

bouncy ride. Chuck Yeager was the first person to break the sound barrier when he flew faster

than the speed of sound in the X-1 rocket-powered aircraft on October 14, 1947.

http://www.senior-lifestyle.com/yeager.html

Shock Wavehttp://observe.phy.sfasu.edu/courses/phy101/lectures101/

http://observe.phy.sfasu.edu/courses/phy101/lectures101/

- slower than the speed of soundSubsonic

Supersonic - faster than the speed of sound

Mach Number =speed of soundspeed of object

Bow and Shock Waves

Shock wave of a bullet piercing a sheet of Plexiglass.

• Look carefully and see the second shock wave originating at the tail of the bullet.

Light deflecting as the bullet passes through the compressed air makes the shock visible.

a shock wave

• Between these two cones, the air pressure rises sharply to above atmospheric pressure, then falls below atmospheric pressure before sharply returning to normal beyond the inner tail cone

• This overpressure suddenly followed by underpressure intensifies the sonic boom.

usually consists of two cones: a high-pressure cone generated at the bow of the supersonic aircraft and a low-pressure cone that follows at the tail of the craft.

The shock wave A graph of the air pressure at ground level between the cones takes the shape of the letter N.

A common misconception is that sonic booms

• The fact is that a shock wave

and its resulting sonic boom

are swept continuously

behind and below an aircraft

traveling faster than sound,

just as a bow wave is swept

continuously behind a

speedboat.

• listener B is in the process of

hearing a sonic boom.

• Listener C has already heard it,

• listener A will hear it shortly.

• The aircraft that generated this

shock wave may have broken

through the sound barrier many

minutes ago!

Sonic Boom

What determines the speed of a wave?

(a) the frequency

(b) the wavelength

(c) the amplitude

(d) the period

(e) the medium of transmission

What dictates the frequency of a sound wave?

(a) wavelength

(b) medium

(c) source of the sound

(d) speed

(e) amplitude

Example Question

The distance from trough to trough on a periodic wave is called its...– a) frequency.– b) period.– c) wavelength.– d) amplitude.

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Example QuestionA train whistle at rest has a frequency of 3000

Hertz. If you are standing still and observe the frequency to be 3010 Hertz, then you can conclude that...– a) the train is moving away from you.– b) the train is moving toward you– c) the sound from the whistle has echoed– d) not enough information is given

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Chapter 20

Sound

Web Page

Sound...• ...a longitudinal wave in air caused by a

vibrating object.

• Demos: – Vortex Box– Card and rotating blades– Oscillator and Speaker

Origin of Sound• infrasonic

– frequencies < 20 Hz

• ultrasonic– frequencies > 20,000 Hz

• human hearing range – frequencies between 20 Hz and 20,000 Hz

Nature of Sound in Air• Sound requires a medium.

– solid, liquid or gas– Demo: Bell in a evacuated Bell Jar

• Sound waves have compression and rarefaction regions.

Origin of Sound• infrasonic

– frequencies < 20 Hz

• ultrasonic– frequencies > 20,000 Hz

• human hearing range – frequencies between 20 Hz and 20,000 Hz

Speed of Sound in Air

• 340 meters/second• 760 miles/hour• Mach 1

• Video Segments– A lumberjack, lightning, and an explosion at a

distance.

increases with increases with humidityhumidityincreases with increases with temperaturetemperatureincreases with increases with densitydensity

How it varies:How it varies:

SPEED OF SOUND

Lightning and Thunder

What is the approximate distance of a thunderstorm when you note a 3 second delay between the flash of the lightning and the sound of the thunder?

Answer: 3 seconds 340 meters/second= 1020 meters

Acoustics...

• ...the study of sound properties.

• When a sound wave strikes a surface it can be.…– (a) reflected.– (b) transmitted.– (c) absorbed.– (d) all of these.

Reflection of Sound• e.g. an echo

• Reverberation - re-echoed sound, multiple reflections of sound waves from walls

• Compare reflections from a hard wall with that from a carpet wall.

Demo: Whip

Refraction of Sound• Refraction - the bending of a wave

• Sound travels faster in warm air than in cool air.

• Sound waves bend toward cooler air.

Desert and Lake Example

Forced Vibrations...• …the setting up of vibrations in an object by

a vibrating force.

• Examples of Forced Vibration:– A tuning fork touching a wood surface– Sounding boards for stringed instruments– Matching tuning fork boxes

Natural Frequency...• …the frequency at which an elastic object

naturally tends to vibrate.

• At this frequency, a minimum energy is required to produce a forced vibration.

Natural Frequency...• The natural frequency of a body depends

on its ...– elasticity– size– shape

Natural Frequency Examples• Mass on a Spring • Ringing Small and Large Bells• Xylophone • Singing Rod• Rubbing a Wine Glass• Dropping Aluminum Rods• Boom Whackers• Organ Pipe• Ruben’s Tube (http://www.youtube.com/watch?v=HpovwbPGEoo)

http://www.youtube.com/watch?v=HpovwbPGEoo

Resonance...• …is the result of forced vibrations in a body

when the applied frequency…• ...matches the natural frequency of the body.

• The resulting vibration has a high amplitude and can destroy the body that is vibrating.

Resonance Demos

• Chinese Spouting Bowl• Tibetan Bowl• PVP Pipes• Iron Tube

Examples of Resonance• mass on a spring at resonance• swinging your legs in a swing• breaking a wine glass using sound• a singing rod caused by forced vibration• fog horn • a tuning fork exciting a guitar string

– http://observe.phy.sfasu.edu/courses/phy101/lectures101/Movies/

• In 1940, the Tacoma Narrows Bridge was destroyed by wind-generated resonance.

http://observe.phy.sfasu.edu/courses/phy101/lectures101/Movies/

• Imagine you’re sitting on a swing and want

to go higher. You pump your legs at a

certain rate to increase your swinging.

• This is an example of you creating resonance

by matching the frequency of the swing.

Resonance allows energy to be transferred to a vibrating object

efficiently if the energy is delivered at the natural frequency of vibration.

Tacoma Narrows Bridge

Sound Interference• Overlapping compressions of a sound wave will result

in…– …constructive interference.– …and a louder sound.

• Overlapping a compression and a rarefaction results in... – …destructive interference.– …and a softer sound.

Constructive InterferenceDestructive Interference

Constructive Interference occurs when waves are in phase, that is when crests are superimposed and

troughs are superimposed.

Destructive interference occurs when waves are out of phase, that is when crests are superimposed with

troughs.

10. SHOCK WAVES

• Just as circular waves move out from a swimming bug, spherical waves move out from a flying object. If the object flies faster than the waves, the result is a cone-shaped shock wave.

• Demo - Cone of Waves• There are two booms, one from the front of the flying object

and one from the back.

9. BOW WAVES

• Waves in front of moving object pile up.• Slide - Wave Barrier• Slide - “Bow” Wave• The familiar bow wave generated by a speedboat knifing

through the water is a non-periodic wave produced by the overlapping of many periodic circular waves. It has a constant shape.

10. SHOCK WAVES

• Just as circular waves move out from a swimming bug, spherical waves move out from a flying object. If the object flies faster than the waves, the result is a cone-shaped shock wave.

• Demo - Cone of Waves• There are two booms, one from the front of the flying object

and one from the back.

Demo - Crack whip

• Video - FB-111 Sonic Boom

• MPEG - FS14 Sonic Boom

• Word Doc - Sonic Boom

• The boom is not produced just when the flying

object “breaks” through the sound barrier.

- slower than the speed of soundSubsonic

• Supersonic - faster than the speed of sound

Mach Number =speed of sound

speed of object

• Beats - the periodic variation in loudness of two sounds played together

• The beat frequency is equal to the difference in the frequency of the two sounds.

• What is the beat frequency when a 262 Hz and a 266 Hz tuning fork are sounded together?

Radio Broadcasts• Modulation - an impression of the sound wave on a

higher frequency radio wave

• AM – Amplitude Modulation

• 535 kHz to 1605 kHz

• FM – Frequency Modulation

• 88 MHz to 108 MHz

Constructive Interference occurs when waves are in phase, that is when crests are superimposed

and troughs are superimposed.

Destructive interference occurs when waves are out of phase, that is when crests are

superimposed with troughs.

Once an object is moving faster than the speed of sound, it will make sound

• A supersonic bullet passing overhead produces a crack, which is a small sonic boom.

• If the bullet were larger and disturbed more air in its path, the crack would be more boomlike.

• When a lion tamer cracks a circus whip, the cracking sound is actually a sonic boom produced by the tip of the whip when it travels faster than the speed of sound.

• Both the bullet and the whip are not in themselves sound sources, but, when traveling at supersonic speeds, they produce their own sound as they generate shock waves.

vibrations & waves 19 & 20 sound in a vacuum sound is the propagation of vibrations through...

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