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Vibrations and Waves

• Vibration—“a wiggle in time”

• Wave—“a wiggle in space and time”; a disturbance that

travels through a medium from one location to another

location

• Back and forth vibratory motion = oscillatory motion.

– The oscillatory motion of a pendulum is an instance of

simple harmonic motion.

• Period—the time of a back and forth swing. (Time/vibrations)

– Depends only on the length of the pendulum and the

acceleration of gravity.

– A pendulum makes 20 vibrations in 40 seconds. Calculate

its period.

Wave Description• A pendulum swinging over a moving piece of paper

will trace out a sine curve.

• Wavelength—the distance between successive identical parts of the wave (crest to crest, for instance).

• Frequency—how frequently a vibration occurs.

– A complete back and forth vibration is one cycle.

– Hertz (Hz)—the unit of frequency.• One cycle per second = 1 Hz

• Two cycles per second = 2 Hz

“home”

• The source of all waves is something that vibrates

– The frequency of the vibrating source and the frequency of

the wave it produces is the same.

• If the frequency is known, then the period can be

determined (and vice versa).

Frequency = 1/period

Period = 1/frequency

• Waves transfer energy, not matter between two points.

– The energy is carried by a disturbance in the medium, not by

matter moving from one point to the other.

Wave Motion

• What do trials 1-5 tell you?

• What about trials 6-8?

Wave Speed

• The speed of a wave depends on the medium through which it is moving.

– Sound travels through air at ~ 330 m/s

– Sound travels 4 times faster in water.

• Wave speed = frequency x wavelength

v = fλ

• If they are produced at the same time, high frequency sounds (small wavelength) reach your ears at the same time as low frequency sounds (large wavelengths).

Wave recap

• "a wave is a disturbance moving through a

medium.“

• Medium could be water, air, a rope, a slinky and

are distinguished by their properties (material,

density, temperature, elasticity, ect)

– These properties describe the material not the wave

itself

• Waves are distinguished from each other based on

amplitude, frequency, wavelength

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Wave speed

• wave speed depends upon the medium

through which the wave is moving. Only an

alteration in the properties of the medium

will cause a change in the speed.

CYU

TRUE or FALSE:

• Doubling the frequency of a wave source

doubles the speed of the waves.

Solve for wave speed Solve for wave speed

3.5 m/s

3.5 m/s

2.5 m/s

2.5 m/s

2.1 m/s

2.2 m/s

CYU• As the wavelength of a wave in a uniform medium

increases, its speed will ____

– Decrease

– Increase

– Remain the same

• As the wavelength of a wave in a uniform medium

increases, its frequency will ____

– Decrease

– Increase

– Remain the same

CYU• As the wavelength of a wave in a uniform medium

increases, its speed will ____

– Remain the same, the speed of a wave is not affected by

the wavelength of the wave

• As the wavelength of a wave in a uniform medium

increases, its frequency will ____

– Decrease, wavelength and frequency are inversely

proportional to each other

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• The water waves below are traveling along the surface of

the ocean at a speed of 2.5 m/s and splashing periodically

against Wilbert's perch. Each adjacent crest is 5 meters

apart. The crests splash Wilbert's feet upon reaching his

perch. How much time passes between each successive

drenching? Answer and explain using complete sentences.

Answer to previous slide

• If the wave travels 2.5 meters in one second

then it will travel 5.0 meters in 2.0 seconds.

If Wilbert gets drenched every time the

wave has traveled 5.0 meters, then he will

get drenched every 2.0 seconds.

Transverse and Longitudinal Waves

• Transverse wave—the

motion of the medium is at

right angles to the direction

in which the wave travels.

• Longitudinal wave—the

motion of the medium is

along the same direction in

which the medium travels.

Reflection – fixed end• Reflection involves a change in direction of waves when they

bounce off a barrier

• Boundary behavior—the behavior of a wave upon reaching the end of a medium.

• Consider a rope fixed to a heavy object at one end.

– The speed of the reflected pulse is the same as the incident pulse.

– The wavelength of the reflected pulse is the same as the wavelength of the incident pulse.

– The amplitude of the reflected pulse is less than the amplitude of the incident pulse (some of the energy was transferred to the other object).

• Consider now a rope that is free at both ends.

– The wave is not inverted in free-end reflections.

Reflection- free endReflection to a different medium

– The transmitted pulse (in the more dense medium) is traveling slower than

the reflected pulse (in the less dense medium)

– The transmitted pulse (in the more dense medium) has a smaller wavelength

than the reflected pulse (in the less dense medium)

– The speed and the wavelength of the reflected pulse are the same as the speed

and the wavelength of the incident pulse (less dense medium)

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Reflection to a different medium 2

– The transmitted pulse (in the less dense medium) is traveling faster than the reflected pulse (in the more dense medium)

– The transmitted pulse (in the less dense medium) has a larger wavelength than the reflected pulse (in the more dense medium)

– The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse

Summary of Boundary Behavior

• The wave speed is always greatest in the least dense medium,

• The wavelength is always greatest in the least dense medium,

• The frequency of a wave is not altered by crossing a boundary,

• The reflected pulse becomes inverted when a wave in a less dense medium is heading towards a boundary with a more dense medium,

• The amplitude of the incident pulse is always greater than the amplitude of the reflected pulse.

Ripple Tank and Reflection

• The diagram at the right depicts a series of straight waves approaching

a long barrier extending at an angle across the tank of water.

• The direction that these wavefronts (straight-line crests) are traveling

through the water is represented by the blue arrow

The Law of Reflection

• The diagram below shows the reflected wavefronts and the

reflected ray.

• the waves will always reflect in such a way that the angle

at which they approach the barrier equals the angle at

which they reflect off the barrier.

Refraction

• Refraction of waves involves a change in

the direction of waves as they pass from one

medium to another.

• Refraction, or the bending of the path of the

waves, is accompanied by a change in speed

and wavelength of the waves.

Refraction

• Waves that pass from deep water into

shallow water will refract (bend), slow

down, and their wavelength will decrease.

• What happens to wavelength as wave speed

decreases?

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Refraction Continued

• Light waves also refract when moving into

a different medium.

Diffraction

• Diffraction—a change in direction of waves as they pass through an opening or around a barrier in their path.

• The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength.

– When the wavelength of the waves are smaller than the obstacle, no noticeable diffraction occurs.

Can really be “seen” with sound waves

Interference• More than one vibration or wave can exist at the same

time in the same space.

• Interference pattern—the pattern produced by overlapping waves.

• Constructive interference (reinforcement)—when the crest of one wave overlaps the crest of another.

• Destructive interference (cancellation)—when the crest of one wave overlaps the trough of another.

Interference

• Two overlapping water waves produce an

interference pattern.

– Areas of constructive interference are produced

by waves that are in phase with one another.

– Areas of destructive interference are produces

by waves that are out of phase with one

another.

Heavy lines

represent crests,

light lines represent

troughs.

Which letters represent

constructive interference?

Which ones destructive

interference?

Standing Waves

• Standing wave—a wave in which the nodes

remain stationary.

– Standing waves are produced when two waves of

equal amplitude and wavelength pass through each

other in opposite directions.

– The nodes are stable regions of destructive

interference.

– The positions on a standing wave with the largest

amplitudes are antinodes.

• Consider a bug jiggling in

water.

– The frequency of the waves

produced by a stationary bug will

be the same at points A and B.

– The frequency of the waves

produced by a bug moving

toward B at a speed less than

wave speed will be higher at point

B than point A.

The Doppler Effect

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The Doppler Effect

• When a sound source moves toward you, the

pitch of the sound is greater.

• When a light source moves toward you, the

frequency of the light is increased (blue shift)

– Light from a source moving away from you is red-

shifted.

Bow Waves

• When the speed of the source in a medium is as great as

the speed of the wave it produces, the waves pile up and

create a barrier wave.

• When the source travels faster than the waves it

produces, it outruns the wave crests and creates a V-

shaped bow wave.

– Boats and supersonic aircraft

create bow waves.

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Sound

The Origin of Sound

• All sounds are produced by the vibrations of material objects.

– Vibrating material sends a disturbance through a medium (usually air) in the form of a longitudinal wave.

– Under normal conditions, the frequency of the source = the frequency of the waves produced.

• Pitch—our subjective impression of the frequency of a sound.

– People with normal hearing can perceive pitches with frequencies from 20 Hz to 20,000 Hz.

– Infrasonic—sound waves with frequencies below 20 Hz.

– Ultrasonic—sound waves with frequencies above 20,000 Hz.

Sound in Air and Media that

Transmit Sound

• Compression—a pulse of compressed air.

• Rarefaction—a region (pulse) of low pressure

air.

– Remember: It is the pulse that travels; not the

medium.

• In general, sound is transmitted faster in

liquids than gases, and still faster in solids.

– Sound cannot travel in a vacuum.

The Sonic Spectrum – all

mechanical, longitudinal waves.

Sound Ranges

• Infrasonic – less than 20 Hz

• Ultrasonic – more than 20,000 Hz

• Range of Human Hearing

20 – 20,000 Hz

0 – 120 dB

Driver Type Minimum Frequency Maximum Frequency

Subwoofer < 20Hz 100Hz

Woofer 40Hz 300-3kHz

Mid Woofer 100Hz 3kHz

Midrange 300Hz 3kHz

Tweeter 1.5kHz > 20kHz

Super Tweeter 10kHz 30kHz

Typical Loudspeaker Driver Ranges

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chinchilla 90-22,800

bat 2,000-110,000

beluga whale 1,000-123,000

elephant 16-12,000

porpoise 75-150,000

goldfish 20-3,000

catfish 50-4,000

tuna 50-1,100

bullfrog 100-3,000

tree frog 50-4,000

canary 250-8,000

parakeet 200-8,500

cockatiel 250-8,000

owl 200-12,000

chicken 125-2,000

SpeciesApproximate Range (Hz)

human 64-23,000

dog 67-45,000

cat 45-64,000

cow 23-35,000

horse 55-33,500

sheep 100-30,000

rabbit 360-42,000

rat 200-76,000

mouse 1,000-91,000

opossum 500-64,000

guinea pig 54-50,000

hedgehog 250-45,000

raccoon 100-40,000

ferret 16-44,000

What do these sound like?

• We hear from 20-20000 Hz.

• Will 2000 Hz sound “high” or “low”

pitched?

Speed of Sound

• Distance and time

• Wavelength and frequency

• Characteristics of the material the sound is

traveling in

Speed of Sound

• In air, sound travels about 330 meters per second.

– Water vapor in the air increases this speed slightly.

– Increased temperature also increases this speed.• Each degree increase above 0o C increases the speed of sound by

0.60 m/s.

• Sound travels 4 times faster in water than in air and 15 times faster in steel than in air.

• Sound travels faster through elastic materials than inelastic materials.

– Elasticity—the ability of a material to change shape in response to a force and then regain its initial shape.

• Example: Steel

• Example of an inelastic material: putty

Speed of Sound in Air

Sound Travels Faster in Hotter Air

)60.0(5.331 Cv ×+=

At 25°C

5.346155.331

)2560.0(5.331

=+=

×+=

v

v

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At -25°C

5.316)15(5.331

)2560.0(5.331

=−+=

−×+=

v

v

“tubes”

Decibels – a measure of the

relative intensity of sounds.

Normal Conversation – 60 dB

85 decibels - prolonged exposure can cause gradual hearing loss.

100 decibels - no more than 15 minutes prolonged exposure recommended

110 decibels - regular exposure of more than one minute risks permanent hearing loss

without hearing protection. Loudest Sounds Ever!

• 400,000 Watt speakers 135-

145 decibel

• fireworks 145-150

• dragster 155-160

• Space shuttle 165-170

• blue whale 188

• The Tunguska event 315 June

30, 1908

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Important Decibel Ideas

• This is a “relative” (comparing) scale.

• Humans can distinguish about 1 dB.

• 10dB higher “sounds” 2x louder.

• Logarithmic, not linear.

• 10x more energy = 10dB higher

• 100x more energy = 20dB higher

• 1000x more energy = 30dB higher

• 10,000,000x more energy = 70dB higher

Loudness

• The intensity of a sound is proportional to the square of the amplitude of a sound wave.

– Decibel (db)—the unit of intensity.

• Loudness—a physiological sensation that differs from person to person.

– Loudness varies nearly as the logarithm of intensity.

– 0 db = the lower threshold of hearing for a normal ear.

– 10 db is 10 x more intense than 0 db.

– 20 db is 10 x more intense than 10 db and 100 x more intense than 0 db.

Beats Two similar sounds played together

Resonance

Natural Frequency of VibrationThe frequency or frequencies at which an object tends to

vibrate with when hit, struck, plucked, strummed or

somehow disturbed is known as the natural frequency of

the object.

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Forced Vibration

Chalkboard – Tuning

Fork

Resonance

Tacoma Narrows Bridge

• http://youtu.be/3mclp9QmCGs

Resonance Examples

• Breaking Wine Glass

• http://www.youtube.com/watch?v=17tqXgv

CN0E&feature=related

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