Vibrations and WavesVibrations and Waves

Chapter 11Chapter 11

Simple Harmonic MotionSimple Harmonic Motion

Chapter 11 Section 1Chapter 11 Section 1

Periodic MotionPeriodic Motion

Any repetitive, or cyclical, types of Any repetitive, or cyclical, types of motionmotion– Examples?Examples?

Simple Harmonic MotionSimple Harmonic Motion is a specialized is a specialized form of periodic motionform of periodic motion

Simple Harmonic MotionSimple Harmonic Motion

Periodic vibration around an Periodic vibration around an equilibrium positionequilibrium position

Restoring force must be Restoring force must be

–proportional to displacement proportional to displacement from equilibriumfrom equilibrium

–in the direction of equilibriumin the direction of equilibrium

Restoring ForceRestoring Force

The push or pull that brings the The push or pull that brings the mass back towards equilibriummass back towards equilibrium–The restoring force of a pendulum The restoring force of a pendulum

is a component of the bob’s weight.is a component of the bob’s weight.

–The restoring force for a mass-The restoring force for a mass-spring system is from the stretch (or spring system is from the stretch (or compression) of the springcompression) of the spring

Simple Harmonic MotionSimple Harmonic Motion

Common examples include a Common examples include a mass-spring system or a mass-spring system or a pendulum pendulum –For a pendulum, SHM only for small For a pendulum, SHM only for small

angles (within 10 degrees of angles (within 10 degrees of vertical)vertical)

Describe speed, acceleration, and restoring force at each point.

Describe speed, acceleration, and restoring force at each point.

Virtual Simple Harmonic MotionVirtual Simple Harmonic Motion

http://phet.colorado.edu/simulations/sims.php?sim=Pendulum_Lab

http://phet.colorado.edu/simulations/sims.php?sim=Masses_and_Springs

Measuring Simple Harmonic Measuring Simple Harmonic MotionMotion

Chapter 11 Section 2Chapter 11 Section 2

AmplitudeAmplitude

The maximum displacement The maximum displacement from equilibrium.from equilibrium.

PeriodPeriod

The time it takes for one complete cycle of The time it takes for one complete cycle of motion.motion.

Represented by the symbol TRepresented by the symbol T

Unit of secondsUnit of seconds

FrequencyFrequency

The number of cycles completed in a unit The number of cycles completed in a unit of time (usually seconds)of time (usually seconds)

Represented by the symbol fRepresented by the symbol f

Unit of sUnit of s-1 -1 (also known as Hertz)(also known as Hertz)

Period and FrequencyPeriod and Frequency

Period and frequency are inversely Period and frequency are inversely related.related.

f = 1/T and T = 1/ff = 1/T and T = 1/f

A mass spring system completes A mass spring system completes 10 cycles each second.10 cycles each second.

What is the period?What is the period?– 1/10 s1/10 s

What is the frequency?What is the frequency?– 10 cycles per second (10 Hz)10 cycles per second (10 Hz)

Factors Affecting PendulumsFactors Affecting Pendulums

For small amplitudes, the period of a pendulum For small amplitudes, the period of a pendulum does not depend on the mass or amplitude.does not depend on the mass or amplitude.

Length does affect the period of a pendulum.Length does affect the period of a pendulum.

Factors Affecting Mass-Spring Factors Affecting Mass-Spring SystemsSystems

The heavier the mass, the longer the period The heavier the mass, the longer the period (more inertia)(more inertia)

The stiffer the spring, the less time it will take to The stiffer the spring, the less time it will take to complete one cycle.complete one cycle.

11.2 Problems11.2 Problems

Page 379 allPage 379 all

Page 381 all except for #3 on Section Page 381 all except for #3 on Section ReviewReview

Properties of WavesProperties of Waves

Chapter 11 Section 3Chapter 11 Section 3

Some general terminology…Some general terminology…

PulsePulse – a single disturbance, single cycle – a single disturbance, single cycle

Periodic wavePeriodic wave – continuous, repeated – continuous, repeated disturbancesdisturbances

Sine waveSine wave – a wave whose source vibrates with – a wave whose source vibrates with simple harmonic motionsimple harmonic motion

Medium Medium – whatever the– whatever the

wave is traveling throughwave is traveling through

Wave MotionWave MotionA wave is the motion of energy away from a A wave is the motion of energy away from a source of periodic disturbance.source of periodic disturbance.

Mechanical wavesMechanical waves require a physical medium to require a physical medium to travel through.travel through.– Examples: sound, disturbance in a slinkyExamples: sound, disturbance in a slinky

Examples of physical Examples of physical mediamedia are water, air, are water, air, string, slinky.string, slinky.

Electromagnetic wavesElectromagnetic waves

Do not require a physical medium.Do not require a physical medium.

Examples include x-rays, visible light, radio Examples include x-rays, visible light, radio waves, etc.waves, etc.

Transverse WavesTransverse WavesParticles of the medium move perpendicular to Particles of the medium move perpendicular to the direction of energy transferthe direction of energy transfer

You should be able to identify You should be able to identify crestscrests, , troughstroughs, , wavelengthwavelength (distance traveled during one full (distance traveled during one full cycle), and cycle), and amplitudeamplitude

Crest

Trough

Longitudinal WavesLongitudinal Waves

Particles of the medium move parallel to the Particles of the medium move parallel to the direction of energy transfer (slinky demo)direction of energy transfer (slinky demo)

Be able to Identify Be able to Identify compressionscompressions, , rarefactionsrarefactions, , wavelengthswavelengths

Compressions Rarefactions

Waves transfer energyWaves transfer energy

Note that, while energy is transferred from point A Note that, while energy is transferred from point A to point B, the particles in the medium do not to point B, the particles in the medium do not move from A to B. move from A to B. – Individual particles of the medium merely Individual particles of the medium merely

vibrate back and forth in simple harmonic vibrate back and forth in simple harmonic motionmotion

The rate of energy transfer is proportional to The rate of energy transfer is proportional to the square of the amplitudethe square of the amplitude– When amplitude is doubled, the energy carried When amplitude is doubled, the energy carried

increases by a factor of 4. increases by a factor of 4.

Wave speedWave speedWave speed is determined completely by the Wave speed is determined completely by the characteristics of the mediumcharacteristics of the medium– For an unchanging medium, wave speed is constantFor an unchanging medium, wave speed is constant

Calculate speed of a wave by multiplying wavelength by frequency.Calculate speed of a wave by multiplying wavelength by frequency.– v = f x λ

Practice #1Practice #1

Q: Microwaves travel at the speed of light, Q: Microwaves travel at the speed of light, 3.003.00101088 m/s. When the frequency of m/s. When the frequency of microwaves is 9.00 microwaves is 9.00 101099 Hz, what is their Hz, what is their wavelength?wavelength?

A: 0.0300 mA: 0.0300 m

Practice #2Practice #2

Q: The piano string tuned to middle C Q: The piano string tuned to middle C vibrates with a frequency of 264 Hz. vibrates with a frequency of 264 Hz. Assuming the speed of sound in air is 343 Assuming the speed of sound in air is 343 m/s, find the wavelength of the sound m/s, find the wavelength of the sound waves produced by the string.waves produced by the string.

A: 1.30 mA: 1.30 m

11.3 Problems11.3 Problems

Page 387 1-4Page 387 1-4

Page 388 1-5Page 388 1-5

Wave InteractionsWave Interactions

Chapter 11 Section 4Chapter 11 Section 4

InterferenceInterferenceThe combination of two or more waves in a medium at the same time.The combination of two or more waves in a medium at the same time.– Matter cannot occupy the same space at the same time, but energy can.Matter cannot occupy the same space at the same time, but energy can.

The The Superposition Principle Superposition Principle describes what happens when waves describes what happens when waves interfere…interfere…– Waves (energy) pass through each other completely unaffectedWaves (energy) pass through each other completely unaffected– The medium will be displaced an amount equal to the vector sum of what the The medium will be displaced an amount equal to the vector sum of what the

waves would have done individuallywaves would have done individually

Constructive InterferenceConstructive Interference

Waves are on the same Waves are on the same side of equilibrium.side of equilibrium.

Waves meet, combine Waves meet, combine according to the according to the superposition principle, superposition principle, and pass through and pass through unchanged.unchanged.

Amplitude larger than Amplitude larger than originalsoriginals

Destructive InterferenceDestructive Interference

Waves are on the Waves are on the opposite sides of opposite sides of equilibrium.equilibrium.

Waves meet, combine Waves meet, combine according to the according to the superposition principle, superposition principle, and pass through and pass through unchanged.unchanged.

Amplitude smaller than Amplitude smaller than at least one original at least one original wavewave

Complete Destructive InterferenceComplete Destructive Interference

Interference patternsInterference patterns

Interference Interference patterns result patterns result from continuous from continuous interference.interference.

Check it out!

ReflectionReflection

The bouncing of a wave when it The bouncing of a wave when it encounters the boundary between two encounters the boundary between two different mediadifferent media

Fixed End ReflectionFixed End Reflection

At a fixed boundary, waves are inverted as they At a fixed boundary, waves are inverted as they are reflected.are reflected.

Free End ReflectionFree End Reflection

At a free boundary, waves are reflected on the At a free boundary, waves are reflected on the same side of equilibriumsame side of equilibrium

Standing WavesStanding Waves

A wave pattern that results when two waves of A wave pattern that results when two waves of the same frequency, wavelength, and amplitude the same frequency, wavelength, and amplitude travel in opposite directions and interfere.travel in opposite directions and interfere.

Standing wave partsStanding wave parts

NodeNode – point that maintains zero displacement – point that maintains zero displacement

AntinodeAntinode – point at which largest displacement – point at which largest displacement occursoccurs

Standing wavesStanding waves

Only certain frequencies produce standing Only certain frequencies produce standing wave patterns. wave patterns.

If a string is 4.0 m long, what are If a string is 4.0 m long, what are three wavelengths that will produce three wavelengths that will produce

standing waves on this string?standing waves on this string?