Vibrations and WavesVibrations and Waves

Chapter 25Chapter 25

Vibration of a PendulumVibration of a Pendulum Vibration – Vibration – a wiggle in timea wiggle in time A vibration cannot exist in one instantA vibration cannot exist in one instant, , but needs but needs

time to move back and forthtime to move back and forth Wave – Wave – a wiggle in space and timea wiggle in space and time A wave cannot exist in one place, but must A wave cannot exist in one place, but must

extend from one place to anotherextend from one place to another Period – Period – the time of a back-and-forth swing of a the time of a back-and-forth swing of a

pendulum, depends only on pendulum, depends only on the length of the the length of the pendulum pendulum andand the acceleration of gravity (T = the acceleration of gravity (T = 22π√π√(L/g))(L/g))

A long pendulum has a longer period than a A long pendulum has a longer period than a shorter pendulumshorter pendulum

Wave DescriptionWave Description

Simple Harmonic Motion – Simple Harmonic Motion – the back-and-the back-and-forth vibratory motion of a swinging forth vibratory motion of a swinging pendulumpendulum

When a pendulum is placed over a moving When a pendulum is placed over a moving conveyor belt, which allows a trace of the conveyor belt, which allows a trace of the motion, the pendulum will trace out a motion, the pendulum will trace out a sine sine curvecurve

A A sine curvesine curve is a pictorial representation is a pictorial representation of a waveof a wave

Simple Harmonic MotionSimple Harmonic Motion

Wave DescriptionWave Description Crest – Crest – high point on a wavehigh point on a wave Trough – Trough – low point on a wavelow point on a wave Amplitude – Amplitude – the distance from the midpoint to the distance from the midpoint to

the crestthe crest The amplitude equals the maximum The amplitude equals the maximum

displacement from equilibriumdisplacement from equilibrium Wavelength – Wavelength – the distance from the top of one the distance from the top of one

crest to the top of the next one (or between crest to the top of the next one (or between successive identical parts of the wave)successive identical parts of the wave)

Frequency – Frequency – describes how often a vibration describes how often a vibration occurs, units are in occurs, units are in HertzHertz (Hz = 1 cycle/second) (Hz = 1 cycle/second)

Frequency = 1/Period Frequency = 1/Period (Hz)(Hz)Period = 1/Frequency Period = 1/Frequency (s)(s)

Wave DescriptionWave Description

Wave MotionWave Motion

When energy is transferred by a wave When energy is transferred by a wave from a vibrating source to a distant from a vibrating source to a distant receiver, there is receiver, there is nono transfer of matter transfer of matter between the two pointsbetween the two points

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

Wave MotionWave Motion

Wave SpeedWave Speed The speed of a wave depends on the The speed of a wave depends on the

medium through which it travelsmedium through which it travels Whatever the medium, the speed, Whatever the medium, the speed,

wavelength, and frequency of the wave wavelength, and frequency of the wave are relatedare relatedWave speed = wavelength X frequencyWave speed = wavelength X frequency

(measured in m/s)(measured in m/s)v = v = λλf f

Sound waves move at speeds of about Sound waves move at speeds of about 330 m/s to 350 m/s in air, and four times 330 m/s to 350 m/s in air, and four times faster in waterfaster in water

Wave Speed ProblemWave 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?

Transverse WavesTransverse Waves

Transverse Waves – Transverse Waves – the motion of the the motion of the medium is at right angles to the direction medium is at right angles to the direction in which the wave travelsin which the wave travels

Examples: stretched strings in musical Examples: stretched strings in musical instruments, waves on surfaces of liquids, instruments, waves on surfaces of liquids, radio waves, light waves, and s-waves radio waves, light waves, and s-waves (earthquakes)(earthquakes)

Transverse WavesTransverse Waves

Longitudinal WavesLongitudinal Waves

Longitudinal Waves – Longitudinal Waves – particles move particles move along the direction of the wave rather than along the direction of the wave rather than at right angles to itat right angles to it

Examples: sound waves and p-waves Examples: sound waves and p-waves (earthquakes)(earthquakes)

Longitudinal WavesLongitudinal Waves

InterferenceInterference Interference Pattern – Interference Pattern – within a pattern, wave within a pattern, wave

effects may be increased, decreased, or effects may be increased, decreased, or neutralizedneutralized

Constructive InterferenceConstructive Interference (reinforcement) – (reinforcement) – the crest of one wave overlaps the crest of the crest of one wave overlaps the crest of another, their individual effects add together another, their individual effects add together producing an increased amplitudeproducing an increased amplitude

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

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

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

InterferenceInterference

Standing WavesStanding Waves

Standing Wave –Standing Wave – certain parts of the wave certain parts of the wave remain stationary, when the incident wave and remain stationary, when the incident wave and reflected wave meetreflected wave meet

Nodes –Nodes – part of the standing wave which does part of the standing wave which does not move and has no amplitude (at equilibrium)not move and has no amplitude (at equilibrium)

Antinodes –Antinodes – position on a standing wave which position on a standing wave which has the largest amplitudehas the largest amplitude

When two waves of equal amplitude and When two waves of equal amplitude and wavelength pass through each other in opposite wavelength pass through each other in opposite directions, they are always directions, they are always out of phaseout of phase at the at the nodes and nodes and in phasein phase at the antinodes at the antinodes

Formation of Standing WavesFormation of Standing Waves

The Doppler EffectThe Doppler Effect Doppler Effect – Doppler Effect – the apparent change in frequency the apparent change in frequency

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

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

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

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

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

The Doppler EffectThe Doppler Effect

Blue Shift and Red ShiftBlue Shift and Red Shift

Bow and Shock WavesBow and Shock Waves

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

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

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

Bow and Shock WavesBow and Shock Waves

AssignmentAssignment

Read Chapter 25 (pg. 372-386)Read Chapter 25 (pg. 372-386) Do Chapter 25 Assessment #21-41 Do Chapter 25 Assessment #21-41

(pg. 388-389)(pg. 388-389)