Wave

Transfers Energy Without Transferring Matter

Wave• A wave can be described as a

disturbance that travels through a medium from one location to another location.

There are three types of waves:

• Mechanical waves require a material medium to travel (air, water, ropes).

• Electromagnetic waves do not require a medium to travel (light, radio).

• Matter waves are produced by electrons and particles.

Mechanical Waves• Transverse waves cause the medium

to move perpendicular to the direction of the wave.

• Longitudinal waves cause the medium to move parallel to the direction of the wave.

• Surface waves are both transverse waves and longitudinal waves mixed in one medium. (Such as water waves)

• Torsional waves produce a twisting motion through the medium – such as the ones which caused the collapse of the Tacoma Narrows Bridge.

Tacoma Narrows BridgeTorsional Oscillation

Mechanical Universe Video

Transverse & Longitudinal Waves

• In a transverse wave, the particles of the medium oscillate perpendicular to the direction of wave travel.

• In a longitudinal wave, the particles of the medium oscillate along the direction of wave travel.

3 Types of Mechanical Waves

Wave Tutorial Links• http://library.thinkquest.org/10796/ch8/

ch8.htm

• http://www.physicsclassroom.com/Class/waves/wavestoc.html

Longitudinal Tuning Fork Wave

• Vibrating tines produce an alternating pattern of high pressure and low pressure regions.

• This pattern travels away from the fork.

• Compression – high pressure

• Rarefaction – low pressure

Period: T

• The PERIOD of a wave is the time for a particle of the medium to complete one oscillation.

• The SI unit for period is the second.

Frequency: f• The FREQUENCY of

a wave is the number of cycles per unit time.

• The unit is Hertz (Hz) which is a cycle per second.

• FREQUENCY is also the reciprocal of the period.

1fT

1Tf

Amplitude: A• The AMPLITUDE of a wave is the

maximum distance of a particle from the equilibrium position.

• The SI unit for amplitude is meter

Wavelength: lambda)• The WAVELENGTH

of a wave is the length of one complete cycle.

• It is the distance between two consecutive “in phase” points.

• In phase points are those that are moving in step with each other.

Wave Applets• Wavelength, Amplitude, Phase• Frequency, Wavelength, Speed• Longitudinal Wave• Transverse Wave• Superposition Principle 1• Superposition Principle 2

Wave Equation• The speed of a wave

is equal to the product of the wave’s frequency and wavelength.

• v: wave speed• f: frequency• : wavelength

v f

Speed of Wave on String

Fv

mL

Sound Waves

• The origin of any sound is a vibrating object– Usually the frequency of the sound is the

same as that of the vibrating object• Frequency Range:

Sound: 20 Hz – 20,000 HzUltrasound: >20,000 HzInfrasound: < 20 Hz

Forced Vibration & Resonance

• forced vibration – example -- strike tuning fork and hold the stem against the table

• sounding board -- used to amplify sound in music boxes and all string

• resonance -- when the frequency of forced vibrations matches the object's natural frequency, a dramatic increase in amplitude occurs

Speed of SoundAluminum 6420Granite 6000Steel 5960Pyrex glass 5640Copper 5010Plastic 2680Fresh water (20 ºC) 1482Fresh water (0 ºC) 1402Hydrogen (0 ºC) 1284Helium (0 ºC) 965Air (20 ºC) 343Air (0 ºC) 331

Material Speed (m/s)

Speed of Sound in Air• depends on wind conditions,

temperature, and humidity • does NOT depend on loudness or

frequency of the sound• all sounds travel at the same speed in

the same medium in dry air at 0°C ~ 331 m/s (1200 km/h) (740 mi/h)

• Sound travels faster through warm air than cold air.

• In air, vsound = 331.4 m/s + (0.6 m/s/Co)*TC

Distance to Lightning• Light travels at

3 x 108 m/s in air• Sound travels at

about 330 m/s in air at 0oC

• It takes about 5 seconds for the sound (the thunder) to travel 1 mile.

• Count the seconds between the flash and the sound, divide by 5, and you have the approximate distance in miles to the lightning.

Pitch & Loudness • Pitch – frequency

Double frequency – go up an octave• Loudness – amplitude

– Units – W/m2

*Energy PowerIntensitytime area area

PIA

2Energy Amplitude

Human Ear

Decibel Scale• incredibly sensitive • can hear everything from

fingertip brushing lightly over fabric to a loud jet engine

• sound of jet engine is about 1012 times more powerful than smallest audible sound

• a big difference! • decibel scale -- smallest

audible sound is 0 dB• A sound 10 times more

powerful is 10 dB• A sound 100 times more

powerful than near total silence is 20 dB

Decibel Scale is

logarithmic

Sound IntensitiesLoudest sound produced in laboratory 109

Saturn V rocket at 50 m 108

Rupture of the eardrum 104

Jet engine at 50 m 10Threshold of pain 1Rock concert 10–1

Jackhammer at 1 m 10–3

Heavy street traffic 10–5

Conversation at 1 m 10–6

Classroom 10–7

Whisper at 1 m 10–10

Normal breathing 10–11

Threshold of hearing 10–12

(W/m2)

Intensity Level• Logarithmic Scale

• Dimensionless• I0 = 10-12 W/m2

0

10log II

Decibel Levels• Near total silence - 0 dB • A whisper - 15 dB • Normal conversation - 60 dB • A lawnmower - 90 dB • A car horn - 110 dB • A rock concert or a jet engine - 120

dB • A gunshot or firecracker - 140 dB

Doppler Effect• Doppler Effect Lesson

Doppler Effect• Moving Source Moving

Observer

• General Expression

11

f fuv

1 uf fv

1

1

o

s

uvf f

uv

Superposition Principle• Wave interference occurs when two or

more waves act simultaneously on a medium.

• Whenever two or more waves pass through each other, the resulting disturbance at a given point in the medium may usually be found by adding the individual displacements that each wave would have caused. (Principle of Superposition)

Constructive Interference

• Constructive interference occurs when the waves are trying to displace the medium in the same direction.

Destructive Interference

• When these two waves are completely overlapping, there will be complete destructive interference.

• Destructive interference occurs when the waves are trying to displace the medium in opposite directions.

Pulse/Wave Reflection

• Fixed/Free End Reflection of Sine Wave

Free End ReflectionFixed End Reflection

Interference between incident and reflected pulse in a fixed end reflection

Standing Waves• For certain

frequencies, the interference of the incident and reflected waves results in a standing wave pattern.

Fundamental Frequencyand Harmonics

2

2

fundamental

fundamental

L

vfL

Standing Waves in a Tube

• Closed on one end: 4

4

fundamental

fundamental

L

vfL

• Open on both ends:

2

2

fundamental

fundamental

L

vfL

Waves Moving in and Out of Phase

• When the 2 waves are in phase, the resulting disturbance has a maximum amplitude.

• When the 2 waves are out of phase, the resulting disturbance has a minimum amplitude.

Beats

• Waves of slightly different frequencies form a pattern of alternating maximum and minimum amplitude.

• The packets of maximum amplitude are called beats.

Noise Canceling• tiny microphones, one on each

earpiece, detect ambient noise before it gets to your ears.

• noise-cancellation circuitry inverts the captured signal, turning the noise's sound wave upside down.

• noise-cancellation system adds the sonic opposite of the external noise to whatever you're listening to

• eliminating most of the pollution and leaving you with just your music.

Standing Waves

• http://phet.colorado.edu

Fundamental & Harmonics