WAVES Vibrations that carry energy from one place to another.

WAVESWAVES

Vibrations that carry energy from one Vibrations that carry energy from one place to anotherplace to another

Types of WaveTypes of Wave

Mechanical. Examples: slinky, rope, water, Mechanical. Examples: slinky, rope, water, sound, & earthquakesound, & earthquake

Electromagnetic. Examples: light, radar, Electromagnetic. Examples: light, radar, microwaves, radio, & x-raysmicrowaves, radio, & x-rays

What Moves in a Wave?What Moves in a Wave?

Energy can be transported over long Energy can be transported over long distancesdistances

The medium in which the wave exists has The medium in which the wave exists has only limited movementonly limited movement

Example: Ocean swells from distant stormsExample: Ocean swells from distant storms

Path of each bit of water is ellipse

Periodic WavePeriodic Wave

Source is a continuous vibrationSource is a continuous vibration The vibration moves outwardThe vibration moves outward

Wave Basics - VocabularyWave Basics - Vocabulary

WavelengthWavelength is distance from crest to crest or is distance from crest to crest or trough to troughtrough to trough

AmplitudeAmplitude is maximum height of a crest or depth is maximum height of a crest or depth of a trough relative to equilibrium levelof a trough relative to equilibrium level

Frequency and PeriodFrequency and Period

FrequencyFrequency, f, is number of crests (waves) that pass , f, is number of crests (waves) that pass a given point per seconda given point per second

PeriodPeriod, T, is time for one full wave cycle to pass, T, is time for one full wave cycle to pass T = 1/f f = 1/T (inverses or reciprocals)T = 1/f f = 1/T (inverses or reciprocals) Waves /second = seconds/wave = Waves /second = seconds/wave = f T

Unit of FrequencyUnit of Frequency

Hertz (Hz)Hertz (Hz) SecondSecond-1 -1 same as 1/second or per secondsame as 1/second or per second Used to be “cycles per second”Used to be “cycles per second”

Wave VelocityWave Velocity

Wave velocity,v, is the velocity at which any part Wave velocity,v, is the velocity at which any part of the wave movesof the wave moves

If wavelength = If wavelength = v = v = ff Example: a wave has a wavelength of 10m and a Example: a wave has a wavelength of 10m and a

frequency of 3Hz (three crests pass per second.) frequency of 3Hz (three crests pass per second.) What is the velocity of the wave? Hint: Think of What is the velocity of the wave? Hint: Think of each full wave as a boxcar. What is the speed of each full wave as a boxcar. What is the speed of the train?the train?

v = v = f f v/f f = v/ v/f f = v/ lambdalambdawavelengthwavelength

f frequency f frequency

v is sometimes called v is sometimes called velocity velocity ofof propagation propagation (speed wave (speed wave moves in medium) moves in medium)

ExampleExample

A ocean wave travels from Hawaii at 10 A ocean wave travels from Hawaii at 10 meters/sec. Its frequency is 0.2 Hz. What meters/sec. Its frequency is 0.2 Hz. What is the wavelength?is the wavelength?

= v/f = 10/0.2 = 50 m

Second exampleSecond example

What is the wavelength of 100 MHz FM What is the wavelength of 100 MHz FM radio waves? Use v = c = 3 x 10radio waves? Use v = c = 3 x 1088 m/s m/s

= v/f = 3 x 10= v/f = 3 x 1088 m/s m/s ÷ 100 ÷ 100 x 10x 1066 s s-1-1

= (300 x 10= (300 x 1066)) ÷ (100 ÷ (100 x 10x 1066)) mm = 3.0 m= 3.0 m

Another exampleAnother example

Waves travel 75 m/s on a certain stretched Waves travel 75 m/s on a certain stretched rope. The distance between adjacent crests rope. The distance between adjacent crests is 5.0 m. Find the frequency and the period.is 5.0 m. Find the frequency and the period.

f = v/f = v/ f = 75 m/s f = 75 m/s ÷ 5.0 m = 15 Hz = 15 s÷ 5.0 m = 15 Hz = 15 s-1-1

T =T = 1/15 = 0.066666 s1/15 = 0.066666 s

Longitudinal vs. Transverse Longitudinal vs. Transverse WavesWaves

Transverse: particles of the medium move Transverse: particles of the medium move perpendicular to the motion of the waveperpendicular to the motion of the wave

Longitudinal: vibrations in same direction as waveLongitudinal: vibrations in same direction as wave

Longitudinal WaveLongitudinal Wave

Can be thought of as alternating Can be thought of as alternating compressionscompressions (squeezing) and expansions (squeezing) and expansions or or rarefactionsrarefactions (unsqueezing) (unsqueezing)

Longitudinal WaveLongitudinal Wave

Sound Wave in AirSound Wave in Air

Compressions and rarefactions of air Compressions and rarefactions of air produced by a vibrating objectproduced by a vibrating object

Waves and EnergyWaves and Energy

Waves with large amplitude carry more Waves with large amplitude carry more energy than waves with small amplitudeenergy than waves with small amplitude

ResonanceResonance

Occurs when driving frequency is close to Occurs when driving frequency is close to natural frequency (all objects have natural natural frequency (all objects have natural frequencies at which they vibrate)frequencies at which they vibrate)

Tacoma Narrows bridge on the way to destruction– large amplitude oscillations in a windstorm

InterferenceInterference

Amplitudes of waves in the same place at Amplitudes of waves in the same place at the same time add algebraically (principle the same time add algebraically (principle of superposition)of superposition)

Constructive interference:Constructive interference:

Destructive InterferenceDestructive Interference

Equal amplitudes(complete):Equal amplitudes(complete):

Unequal Amplitudes(partial):Unequal Amplitudes(partial):

ReflectionReflection

Law of reflection:Law of reflection:

Angle of Incidence equals angle of Angle of Incidence equals angle of ReflectionReflection

Hard Reflection of a PulseHard Reflection of a Pulse

Reflected pulse is invertedReflected pulse is inverted

Soft Reflection of a PulseSoft Reflection of a Pulse

Reflected pulse not invertedReflected pulse not inverted

Soft (free-end) ReflectionSoft (free-end) Reflection

Standing WavesStanding Waves

Result from interference and reflection for Result from interference and reflection for the “right” frequencythe “right” frequency

Points of zero displacement - “nodes” (B)Points of zero displacement - “nodes” (B) Maximum displacement – antinodes (A)Maximum displacement – antinodes (A)

Formation of Standing WavesFormation of Standing Waves

Two waves moving in opposite directionsTwo waves moving in opposite directions

Examples of Standing WavesExamples of Standing Waves

Transverse waves on a slinkyTransverse waves on a slinky Strings of musical instrumentStrings of musical instrument Organ pipes and wind instrumentsOrgan pipes and wind instruments Water waves due to tidal actionWater waves due to tidal action

Standing Wave Patterns on a Standing Wave Patterns on a StringString

““Fundamental” = Fundamental” =

First Harmonic or FundamentalFirst Harmonic or Fundamental

Second HarmonicSecond Harmonic

Third HarmonicThird Harmonic

Wavelength vs. StringWavelength vs. Stringlengthlength

String length = How many String length = How many waves?waves?

L =

String length = How many String length = How many waves?waves?

L = 3/2

Wavelength vs. String LengthWavelength vs. String Length

Wavelengths of first 4 harmonicsWavelengths of first 4 harmonics

L

f =v

Frequencies are related by whole Frequencies are related by whole numbersnumbers

ExampleExample ff1 1 = 100 Hz fundamental= 100 Hz fundamental ff2 2 = 200 Hz 2= 200 Hz 2ndnd harmonic harmonic ff3 3 = 300 Hz 3= 300 Hz 3rdrd harmonic harmonic ff4 4 = 400 Hz 4= 400 Hz 4thth harmonic harmonic etcetc Other frequencies exist but their amplitudes Other frequencies exist but their amplitudes

diminish quickly by destructive interferencediminish quickly by destructive interference

Wave velocity on a stringWave velocity on a string

Related only to properties of mediumRelated only to properties of medium Does not depend on frequency of waveDoes not depend on frequency of wave vv2 2 = T/m/l Tension divided by mass per = T/m/l Tension divided by mass per

unit length of stringunit length of string

Standing Waves in Open TubesStanding Waves in Open Tubes

First Three Harmonics in Open First Three Harmonics in Open TubeTube

Amplitudes are largest at the open ends

Amplitudes zero at the nodes

Tube Closed at One EndTube Closed at One End

L/4

L = /4

L = /4

No even harmonics present f = vair/

BeatsBeats

Two waves of similar frequency interfereTwo waves of similar frequency interfere

Beat frequency equals the difference of the two interfering frequencies

AcknowledgementsAcknowledgements

Diagrams and animations courtesy of Tom Diagrams and animations courtesy of Tom Henderson, Glenbrook South High School, Henderson, Glenbrook South High School, IllinoisIllinois