Vibrations & Waves & Sound a periodic motion of the particles of an elastic body or medium in alternately opposite directions from the position of equilibrium

Vibrations & Waves & Vibrations & Waves & SoundSound

‘”‘”a periodic motion of the a periodic motion of the particles of an elastic body or particles of an elastic body or medium in alternately opposite medium in alternately opposite directions from the position of directions from the position of equilibrium when that equilibrium when that equilibrium has been disturbed”equilibrium has been disturbed”

When things vibrate, they move When things vibrate, they move the air and create sound wavesthe air and create sound waves

Music, talking, sirens, etc.Music, talking, sirens, etc.

Vibrations & WavesVibrations & Waves

Transverse WavesTransverse Waves

Wave AnatomyWave Anatomycrest

trough wavelength

wavelength

amplitude

amplitude

nodes

Vibrations & WavesVibrations & Waves

Wavelength - Distance between peaksWavelength - Distance between peaks Amplitude - Max Height above resting Amplitude - Max Height above resting

spotspot Frequency - Number of Nodes-Crests-Frequency - Number of Nodes-Crests-

Troughs/secondTroughs/second Period - Time of a complete vibrationPeriod - Time of a complete vibration Period = 1 / FrequencyPeriod = 1 / Frequency Frequency = 1 / PeriodFrequency = 1 / Period

Vibrations & WavesVibrations & Waves Water Waves Water Waves

– bounce – bounce swimmers up swimmers up and downand down

Sound Waves Sound Waves - move air - move air back and back and forthforth

Wave MotionWave Motion

Consider a pebble thrown in the waterConsider a pebble thrown in the water Creates circular waves that move out Creates circular waves that move out

from the disturbancefrom the disturbance Water moves up and down, the wave Water moves up and down, the wave

moves outward away from the moves outward away from the disturbancedisturbance

Waves carry energy from the impactWaves carry energy from the impact A bug in the water will move and and A bug in the water will move and and

downdown

Wave SpeedWave Speed

Wavelength is distance between peaks

Frequency is number of peaks per second going past a point in the water

Frequency depends on wavelength and how fast the wave moves!!!

Speed = Wavelength x Frequency

Longitudinal or Longitudinal or Transverse?Transverse?

Longitudinal WavesLongitudinal Waves

Wave AnatomyWave Anatomy

rarefaction

compression

wavelength

wavelength

Sound WavesSound Waves

Human HearingHuman Hearing

sound wavesound wave

vibrates ear drumvibrates ear drum

amplified by bonesamplified by bones

converted to nerve impulses converted to nerve impulses in cochleain cochlea


Molecules in the air vibrate about some average position creating the compressions and rarefactions. We call the frequency of sound the pitch.


PitchPitch highness or highness or

lowness of a lowness of a soundsound

depends on depends on frequency of frequency of sound wavesound wave

human range: human range: 20 - 20,000 Hz20 - 20,000 Hz

ultrasonic waves

subsonic waves

B. Human HearingB. Human Hearing

IntensityIntensity volume of soundvolume of sound depends on energy (amplitude) of depends on energy (amplitude) of

sound wavesound wave measured in decibels (dB)measured in decibels (dB)


7080

100110

120

40

1810

0

DECIBEL SCALE


Speed of SoundSpeed of Sound

Depends on the material of the Depends on the material of the vibrating mediumvibrating medium

Sound can vibrate water, wood Sound can vibrate water, wood (speaker enclosures, pianos), metal, (speaker enclosures, pianos), metal, plastic, etc.plastic, etc.

Sound speed in dry air is 330 Sound speed in dry air is 330 meters/second at 0meters/second at 0oo C C

Faster in warm air, slower in coldFaster in warm air, slower in cold Water 4 times faster, steel 15 times Water 4 times faster, steel 15 times

fasterfaster

Wave ReflectionWave Reflection

When a sound wave reflects from a When a sound wave reflects from a surface we generate an echosurface we generate an echo

Wave reflection from surfaces Wave reflection from surfaces depends on the characteristics of depends on the characteristics of the surfacethe surface

Smooth hard surfaces reflect bestSmooth hard surfaces reflect best Rough soft surfaces reflect poorlyRough soft surfaces reflect poorly Energy not reflected is absorbed or Energy not reflected is absorbed or

transmitted through the materialtransmitted through the material


Think of arrows pointing in the Think of arrows pointing in the direction of the wave motiondirection of the wave motion

We can trace the path of these We can trace the path of these arrowsarrows

Angles Equal


Acoustics of room design is very interesting. Need some reflections to “liven” the room. Too many reflections and the sound gets mushy. Look in a concert hall or auditorium to see the different sound treatments

Wave RefractionWave Refraction

If there is a change in the If there is a change in the characteristics of a medium, waves are characteristics of a medium, waves are bentbent

This occurs because different parts of This occurs because different parts of the wave front travel at different speedsthe wave front travel at different speeds

Think of a marching around a curved Think of a marching around a curved tracktrack

The inside people have to move more The inside people have to move more slowly than the outside people to keep slowly than the outside people to keep the lines straightthe lines straight

Wave RefractionWave Refraction

Wave Reflection & Wave Reflection & RefractionRefraction

The combination of reflection The combination of reflection and refraction enables imagingand refraction enables imaging

Ultrasonic medical imagingUltrasonic medical imaging Naval SONAR for detecting Naval SONAR for detecting

submarinessubmarines Bats catch mosquitoesBats catch mosquitoes Catch discussion of dolphins on Catch discussion of dolphins on

p. 261p. 261

Natural FrequenciesNatural Frequencies

Objects have “natural” Objects have “natural” frequencies based on their size frequencies based on their size and structureand structure

Guitar strings are an exampleGuitar strings are an example Timpani headsTimpani heads Air columnsAir columns

Forced VibrationsForced Vibrations

Can externally impose a vibration Can externally impose a vibration on an objecton an object

Guitars and violins and pianosGuitars and violins and pianos Set the wood into motion at the Set the wood into motion at the

frequency of the stringfrequency of the string This provides a larger surface to This provides a larger surface to

interact with the airinteract with the air Harp vs. PianoHarp vs. Piano

ResonanceResonance

When the forced vibration matches a When the forced vibration matches a natural frequency we get a natural frequency we get a “resonance” condition“resonance” condition

Think about a swing on a playgroundThink about a swing on a playground You go high when you pump the swing You go high when you pump the swing

at its natural vibration frequencyat its natural vibration frequency Sympathetic vibrations in tuning forksSympathetic vibrations in tuning forks Famous Tacoma Narrows bridge Famous Tacoma Narrows bridge

collapsecollapse

Next TimeNext Time

We continue the chapter on waves We continue the chapter on waves and sound.and sound.

Wave InterferenceWave Interference

Principle of SuperpositionPrinciple of Superposition Works for both longitudinal Works for both longitudinal

waves and for transverse waveswaves and for transverse waves


Simply align the waves in time and Simply align the waves in time and add the amplitudesadd the amplitudes

Amplitudes can be either positive or Amplitudes can be either positive or negativenegative

If the amplitudes are of the same If the amplitudes are of the same sign, the wave is reinforced and sign, the wave is reinforced and grows biggergrows bigger

If the amplitudes are of opposite If the amplitudes are of opposite sign, the wave is diminished and sign, the wave is diminished and grows smallergrows smaller




So far, we have only looked at So far, we have only looked at waves that have the same waves that have the same wavelength or frequencywavelength or frequency

What happens if the frequencies What happens if the frequencies are different?are different?

According to the Superposition According to the Superposition Principle, we simply add the two Principle, we simply add the two waves together to see what waves together to see what resultsresults


Produces “Beats”Produces “Beats” This is how musicians “tune” their This is how musicians “tune” their

instruments to match in the instruments to match in the orchestraorchestra


10% Frequency Difference

20% Frequency Difference

Standing WavesStanding Waves

Standing WavesStanding Waves

C. Doppler EffectC. Doppler Effect

Doppler EffectDoppler Effect change in wave change in wave

frequency caused by a frequency caused by a moving wave sourcemoving wave source

moving toward you - moving toward you - pitch sounds higherpitch sounds higher

moving away from you moving away from you - pitch sounds lower- pitch sounds lower

Doppler EffectDoppler Effect

Wave BarriersWave Barriers

The object is moving at the speed of waves in the medium.

See how the waves pile up at the source.

Shock WavesShock Waves

The source is moving faster than the wave speed in the medium.

A shock wave is formed and it is very difficult to break through the previous wave barrier.

These waves produce sonic booms.

Music vs. NoiseMusic vs. Noise

MusicMusic specific pitches and sound qualityspecific pitches and sound quality regular patternregular pattern

NoiseNoise no definite pitchno definite pitch no set patternno set pattern

Guitar StringsGuitar Strings

Guitar StringsGuitar Strings

A combination wave composed of the 1st harmonic and the third harmonic.

MusicMusic

What makes instruments unique is What makes instruments unique is the combination of harmonics the combination of harmonics produced by the different produced by the different instruments.instruments.

Flutes produce primarily the 1st Flutes produce primarily the 1st harmonicharmonic

They have a very pure toneThey have a very pure tone Oboes produce a broad range of Oboes produce a broad range of

harmonics and sound very differentharmonics and sound very different

Combining Waves Combining Waves RevisitedRevisited

Combining WavesCombining Waves

Musical InstrumentsMusical Instruments

Three ways to make soundThree ways to make sound Vibrate a stringVibrate a string Vibrate an air columnVibrate an air column Vibrate a membraneVibrate a membrane

Vibrating StringsVibrating Strings

Violin, viola, cello, string bassViolin, viola, cello, string bass GuitarsGuitars UkulelesUkuleles MandolinsMandolins BanjosBanjos All vibrate a structure to amplify All vibrate a structure to amplify

the soundthe sound

Vibrating Air ColumnsVibrating Air Columns

Pipe OrgansPipe Organs Brass InstrumentsBrass Instruments WoodwindsWoodwinds WhistlesWhistles

Vibrating MembranesVibrating Membranes

Percussion InstrumentsPercussion Instruments Snare DrumSnare Drum Bass DrumBass Drum BongosBongos Timpani are unique in that they are Timpani are unique in that they are

tuned to produce particular 1st tuned to produce particular 1st harmonicsharmonics

You see the timpanist tunes each You see the timpanist tunes each drum during a performancedrum during a performance

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Vibrations & Waves & Sound a periodic motion of the particles of an elastic body or medium in alternately opposite directions from the position of equilibrium