 # WAVES Vibrations (disturbances) that carry energy from one place to another Presentation 2003 Philip M. Dauber as Modified by R. McDermott.

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WAVES Vibrations (disturbances) that carry energy from one place to another Presentation 2003 Philip M. Dauber as Modified by R. McDermott

What Does a Wave Move? Energy can be transported over long distances Energy can be transported over long distances The medium in which the wave exists has only limited movement The medium in which the wave exists has only limited movement Example: Ocean swells from distant storms Example: Ocean swells from distant storms Path of each bit of water is ellipse

Waves Require a Medium A medium is anything with mass A medium is anything with mass A medium may be solid, liquid, or gas A medium may be solid, liquid, or gas The particles of the medium move very small distances from their rest position The particles of the medium move very small distances from their rest position The particles repeat their motion (periodic or harmonic motion) The particles repeat their motion (periodic or harmonic motion)

Periodic Wave Source is a continuous vibration Source is a continuous vibration The vibration moves outward (but mass does not) The vibration moves outward (but mass does not)

Wave Basics Wavelength is distance from crest to crest or trough to trough Wavelength is distance from crest to crest or trough to trough Amplitude is maximum height of a crest or depth of a trough relative to equilibrium level Amplitude is maximum height of a crest or depth of a trough relative to equilibrium level

Wave Basics (cont.) Wavelength is the distance between points “in phase” Wavelength is the distance between points “in phase” A-F, B-G, C-H, D-I, and E-J are “in phase” A-F, B-G, C-H, D-I, and E-J are “in phase”

Frequency and Period Frequency, f, is number of crests that pass a given point per second (measured in hertz) Frequency, f, is number of crests that pass a given point per second (measured in hertz) Period, T, is time for one full wave cycle to pass Period, T, is time for one full wave cycle to pass T = 1/f f = 1/T T = 1/f f = 1/T

Wave Velocity Wave velocity, v, is the velocity at which any part of the wave moves Wave velocity, v, is the velocity at which any part of the wave moves If wavelength =  v = f If wavelength =  v = f Example: a wave has a wavelength of 10m and a frequency of 3Hz (three crests pass per second.) What is the velocity of the wave? Hint: Think of each full wave as a boxcar. What is the speed of the train? Example: a wave has a wavelength of 10m and a frequency of 3Hz (three crests pass per second.) What is the velocity of the wave? Hint: Think of each full wave as a boxcar. What is the speed of the train?

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

Longitudinal vs. Transverse Waves Transverse: particles of the medium move perpendicular to the motion of the wave Transverse: particles of the medium move perpendicular to the motion of the wave Longitudinal: vibrations in same direction as wave Longitudinal: vibrations in same direction as wave

Longitudinal Wave Can be thought of as alternating compressions and expansions or rarefactions Can be thought of as alternating compressions and expansions or rarefactions

Longitudinal Wave Sound is a longitudinal wave

Sound Wave in Air Compressions and rarefactions of air produced by a vibrating object Compressions and rarefactions of air produced by a vibrating object

Transverse Wave The transverse wave below is traveling toward point P The transverse wave below is traveling toward point P How will point P move? How will point P move? Demo

Waves and Energy Waves with large amplitude carry more energy than waves with small amplitude Waves with large amplitude carry more energy than waves with small amplitude Sound amplitude is loudness Sound amplitude is loudness Light amplitude is brightness Light amplitude is brightness

Resonance Occurs when driving frequency is close to natural frequency (all objects have natural frequencies at which they vibrate) Occurs when driving frequency is close to natural frequency (all objects have natural frequencies at which they vibrate) Tacoma Narrows bridge on the way to destruction– large amplitude oscillations in a windstorm Demo

Wave Actions Reflection Reflection Interference Interference Refraction Refraction Diffraction Diffraction Doppler Effect Doppler Effect Polarization (transverse only) Polarization (transverse only)

Reflection Law of reflection: Law of reflection: Angle of incidence equals angle of reflection Angle of incidence equals angle of reflection ii rr

Hard Reflection of a Pulse Fixed endpoint Fixed endpoint Reflected pulse is inverted Reflected pulse is inverted

Soft Reflection of a Pulse Free endpoint Free endpoint Reflected pulse not inverted Reflected pulse not inverted Demo

Interference Amplitudes of two (or more) waves in the same place at the same time add algebraically (principle of superposition) Amplitudes of two (or more) waves in the same place at the same time add algebraically (principle of superposition) Constructive interference: Constructive interference:

Destructive Interference Equal amplitudes: Equal amplitudes: Unequal Amplitudes: Unequal Amplitudes: Demo

Standing Waves Result from interference and reflection for the “right” frequency Result from interference and reflection for the “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 Waves Two waves moving in opposite directions Two waves moving in opposite directions

Examples of Standing Waves Transverse waves on a slinky Transverse waves on a slinky Strings of musical instrument Strings of musical instrument Organ pipes and wind instruments Organ pipes and wind instruments Water waves due to tidal action Water waves due to tidal action Demo

Standing Wave Patterns on a String “Fundamental” = “Fundamental” = 2 nd Harmonic = 2 nd Harmonic = 3 rd Harmonic = 3 rd Harmonic =

First Harmonic or Fundamental

Second Harmonic

Third Harmonic

Wavelength vs. String length

String length = How many waves? L =

String length = How many waves? L = 3/2 

Wavelength vs. String Length Wavelengths of first 4 harmonics Wavelengths of first 4 harmonics

Frequencies are related by whole numbers Example Example f 1 = 100 Hz fundamental f 1 = 100 Hz fundamental f 2 = 200 Hz 2 nd harmonic f 2 = 200 Hz 2 nd harmonic f 3 = 300 Hz 3 rd harmonic f 3 = 300 Hz 3 rd harmonic f 4 = 400 Hz 4 th harmonic f 4 = 400 Hz 4 th harmonic etc etc Other frequencies exist but their amplitudes diminish quickly by destructive interference Other frequencies exist but their amplitudes diminish quickly by destructive interference

Wave velocity on a string Related only to properties of medium Related only to properties of medium Does not depend on frequency of wave Does not depend on frequency of wave v 2 = T/m/l Tension divided by mass per unit length of string v 2 = T/m/l Tension divided by mass per unit length of string

First Three Harmonics in Open Tube Amplitudes are largest at the open ends Amplitudes zero at the nodes

Tube Closed at One End L  /4 L =  /4 L =  /4 No even harmonics present f = v air /

Pressure in Closed Tubes

Beats Two waves of similar frequency interfere Two waves of similar frequency interfere Beat frequency equals the difference of the two interfering frequencies

Refraction Wave moves from one medium into another Wave moves from one medium into another The speed of the wave changes The speed of the wave changes The wavelength of the wave changes The wavelength of the wave changes The frequency of the wave stays the same The frequency of the wave stays the same The wave changes direction The wave changes direction

Refraction Angle of incidence  angle of refraction (generally) Angle of incidence  angle of refraction (generally)

Reflection/Refraction in Rope Notice what happens to amplitude, phase, and wavelength: Notice what happens to amplitude, phase, and wavelength:

Diffraction Part of wave hits a barrier and is cut off Part of wave hits a barrier and is cut off The rest of the wave continues The rest of the wave continues Continuing wave expands behind barrier Continuing wave expands behind barrier Demo

Doppler Effect Observer or source moving Observer or source moving Observed frequency changes Observed frequency changes –If observer and source are closing, frequency is higher than normal –If observer and source are separating, frequency is lower than normal Frequency change for sound is pitch Frequency change for sound is pitch Frequency change for light is color Frequency change for light is color Demo

Polarization Only for transverse waves Only for transverse waves Allows only vibrations in one plane to pass Allows only vibrations in one plane to pass All other planes of vibration are absorbed All other planes of vibration are absorbed Polaroid lenses Polaroid lenses 3D glasses 3D glasses Demo

Acknowledgements Some diagrams and animations courtesy of Tom Henderson, Glenbrook South High School, Illinois Some diagrams and animations courtesy of Tom Henderson, Glenbrook South High School, Illinois

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