Chapter 6 Waves and Sound By Ray Merry Back to home: Back to Physics: .

Chapter 6 Waves and Sound

By Ray MerryBy Ray MerryBack to home: Back to home: www.www.raymerryraymerry.com.com

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Waves in Action:

A Longitudinal Wave, (similar to sound in air)

Wave

A traveling disturbance consisting of A traveling disturbance consisting of coordinated vibrations that carry energy coordinated vibrations that carry energy with no net movement of matter.with no net movement of matter.See pages 217,218,219See pages 217,218,219

Do the Wave! Have you ever "done the wave" as part of a large Have you ever "done the wave" as part of a large

crowd at a football or baseball game? A group of crowd at a football or baseball game? A group of people jump up and sit back down, some nearby people jump up and sit back down, some nearby people see them and they jump up, some people people see them and they jump up, some people further away follow suit and pretty soon you have a further away follow suit and pretty soon you have a wave traveling around the stadium. The wave is the wave traveling around the stadium. The wave is the disturbance (people jumping up and sitting back disturbance (people jumping up and sitting back down), and it travels around the stadium. However, down), and it travels around the stadium. However, none of the individual people the stadium are carried none of the individual people the stadium are carried around with the wave as it travels - they all remain at around with the wave as it travels - they all remain at their seats. their seats.

Wave medium

The wave medium is the substance the The wave medium is the substance the wave is traveling through. wave is traveling through.

E.G. Sound requires a media or material to E.G. Sound requires a media or material to travel through. The media can be water, travel through. The media can be water, air, wood, etc.air, wood, etc.

Light on the other hand travels through a Light on the other hand travels through a vacuum, and may not require a media.vacuum, and may not require a media.

Compare a wave pulse and a continuous wave. A wave pulse is one up and down or back A wave pulse is one up and down or back

and forth motion of a wave (short and and forth motion of a wave (short and fleeting).fleeting).

A continuous wave has many pulses A continuous wave has many pulses (steady (steady and repeating)and repeating) . .

Wave Pulse

Demonstrate both transverse and longitudinal waves on a Slinky, Transverse wave Transverse wave

oscillations are perpendicular (transverse) to the oscillations are perpendicular (transverse) to the direction the wave travels. (p. 219 fig. 6.4 a.)direction the wave travels. (p. 219 fig. 6.4 a.)

Longitudinal wave Longitudinal wave oscillations are along the direction the wave travels. (p. oscillations are along the direction the wave travels. (p. 219 fig. 6.4 b.) note corrections in book p. 219 & 220 219 fig. 6.4 b.) note corrections in book p. 219 & 220

Examples of Waves and Their Type

Longitudinal, Sound in airLongitudinal, Sound in air Transverse, fan wave, sea Transverse, fan wave, sea

wave.wave.

Speed of a wave on a rope depends on its

mass density and the tension applied. = greek letter rho, stands for linear = greek letter rho, stands for linear

densitydensity= linear mass density of a rope, string, = linear mass density of a rope, string, etc. = m/l (mass/length)etc. = m/l (mass/length)

v= (F/v= (F/)½)½ (Speed of a wave on a rope, etc. (Speed of a wave on a rope, etc. = sq. rt. of Force/linear density.)= sq. rt. of Force/linear density.)

Compute the speed of sound in air given the temperature. V= 20.1x(T)V= 20.1x(T)1/21/2 (20.1 x sq.rt of Temp in (20.1 x sq.rt of Temp in

KelvinsKelvins))

Speed of sound waves in air at Speed of sound waves in air at temperature T (SI units, T in Kelvins)temperature T (SI units, T in Kelvins)

Wavelength and Amplitude Amplitude: Maximum displacement of Amplitude: Maximum displacement of

points on a wave, measured from the points on a wave, measured from the equilibrium position. equilibrium position.

Wavelength: (Wavelength: () The distance between two ) The distance between two successive "like" points on a wave. successive "like" points on a wave.

An example is the distance between two An example is the distance between two adjacent peaks or two adjacent valleys.adjacent peaks or two adjacent valleys.

See fig.6.5 p221See fig.6.5 p221

Wavelength vs Amplitude Figurel

WavelengthWavelength

A - AmplitudeA - Amplitude

AA

CrestCrest

TroughTrough

Frequency of a Wave

The number of cycles of a wave The number of cycles of a wave passing a point per unit time. passing a point per unit time.

It equals the number of oscillations per It equals the number of oscillations per second of the wave.second of the wave.

If 15 waves pass a point in 1 second the If 15 waves pass a point in 1 second the frequency f = 15 Hz. frequency f = 15 Hz.

Wave Equation Equation relating the velocity, v, Equation relating the velocity, v,

frequency, f, and wavelength, frequency, f, and wavelength, ,, of a of a continuous wave.continuous wave.

V=fV=f velocity of waves = frequency x velocity of waves = frequency x

wavelength wavelength

Wavefronts and Rays.

See See p 225 fig. 6.11 & fig 6.12 and p 226 p 225 fig. 6.11 & fig 6.12 and p 226 fig. 6.14fig. 6.14

Ray representingdirection of travelof the wave

The Red circle represents wave front

Amplitude of a wave gets smaller farther from the source. The wave energy spreads out in 3 The wave energy spreads out in 3

dimensions, like the surface of a dimensions, like the surface of a sphere.sphere.

As a result the same energy is As a result the same energy is spread out over a larger and larger spread out over a larger and larger surface and amplitude decreases.surface and amplitude decreases.

Define a plane wave.

A wave so far from it’s source that the wave A wave so far from it’s source that the wave front appears to be a straight line.front appears to be a straight line.

Give concrete examples of reflection of waves. Echoes.Echoes.

Parabolic AntennasParabolic Antennas

Doppler effect

The apparent change in frequency of a The apparent change in frequency of a wave due to motion of the source of the wave due to motion of the source of the wave, the receiver, or both. wave, the receiver, or both.

Effects of Movement on f and λ

If the source is moving towards the If the source is moving towards the observer, the observer perceives sound observer, the observer perceives sound waves reaching him or her at a more waves reaching him or her at a more frequent rate (high pitch)frequent rate (high pitch)

If the source is moving away from the If the source is moving away from the observer, the observer perceives sound observer, the observer perceives sound waves reaching him or her at a less frequent waves reaching him or her at a less frequent rate (low pitch). rate (low pitch).

Consequences of the Doppler effect.

pitch of an ambulance or police siren, goes up pitch of an ambulance or police siren, goes up as it approaches and then goes down as it as it approaches and then goes down as it recedes from yourecedes from you

Same effect from a passing train whistle. Same effect from a passing train whistle. Used in astronomy to deduce the component Used in astronomy to deduce the component

of velocity in the line-of-sight of an of velocity in the line-of-sight of an approaching or receding planet/star/galaxy etc. approaching or receding planet/star/galaxy etc.

How it was discovered that the universe is expanding.

Doppler effect was used to determine speed Doppler effect was used to determine speed of galaxies.of galaxies.

They were all found to be moving away They were all found to be moving away from the centerfrom the center

The farther away they were the faster they The farther away they were the faster they seemed to be going away!seemed to be going away!

Cosmology

The study of the structure and evolution The study of the structure and evolution of the universe as a whole.of the universe as a whole.

Hubble relation (or law)

A mathematical expression showing A mathematical expression showing that the farther a galaxy is from us, the that the farther a galaxy is from us, the faster it is moving away. One implication faster it is moving away. One implication of this relation is that the universe is of this relation is that the universe is expanding. expanding.

Echolocation: Radar, Sonar… Process of using the reflection of a Process of using the reflection of a

wave to locate objects. wave to locate objects. We send out a wave, wait for its return.We send out a wave, wait for its return. Since we know the speed and the time, Since we know the speed and the time,

from d=v x t we determine its distance from d=v x t we determine its distance awayaway

Explain what causes a sonic boom. Sound waves build up in front as plane, etc. Sound waves build up in front as plane, etc.

approaches the speed of sound. When it approaches the speed of sound. When it passes the speed of sound they are left passes the speed of sound they are left behind.behind.

Similar to bow waves on a boat.Similar to bow waves on a boat.

Diffraction

The bending of a wave as it passes The bending of a wave as it passes around the edge of a barrier. around the edge of a barrier.

Diffraction causes a wave passing Diffraction causes a wave passing through a gap or a slit to spread out through a gap or a slit to spread out into the shadow regions. into the shadow regions.

See fig. 6.26 p. 232See fig. 6.26 p. 232

Examples of Diffraction

Sound waves traveling around Sound waves traveling around cornerscorners

Water waves going through Water waves going through openings.openings.

Interference The The

consequence consequence of two waves of two waves arriving at the arriving at the same place same place and and combining.combining.

See fig. 6.28 p. See fig. 6.28 p. 233233

Constructive interference occurs occurs

wherever the wherever the two waves two waves meet in phase meet in phase (peak matches (peak matches peak); peak);

the waves add the waves add together. together.

Destructive interference

Destructive interference occurs Destructive interference occurs wherever the two waves meet out of wherever the two waves meet out of phase (peak matches valley); the waves phase (peak matches valley); the waves cancel each other. cancel each other.

Phase and Interference

Give an explanation of how the phase Give an explanation of how the phase relationship of superposed waves relationship of superposed waves determines whether they interfere determines whether they interfere constructively or destructively.constructively or destructively.

In phase is constructive, out of phase 180 In phase is constructive, out of phase 180 degrees (half a cycle) is destructive.degrees (half a cycle) is destructive.

What is sound?

A wave disturbance which our ears are A wave disturbance which our ears are sensitive to. A longitudinal wave in air, if it sensitive to. A longitudinal wave in air, if it is audible it has a frequency between 20 and is audible it has a frequency between 20 and 20,000 hz.20,000 hz.

Does sound occur if there is no one to hear Does sound occur if there is no one to hear it?it?

Sound The back and forth vibrations of the surrounding air The back and forth vibrations of the surrounding air

molecules creates a pressure wave which travels molecules creates a pressure wave which travels outward from its source. This pressure wave consists outward from its source. This pressure wave consists of compressions and rarefactions. The compressions of compressions and rarefactions. The compressions are regions of high pressure, where the air molecules are regions of high pressure, where the air molecules are compressed into a small region of space. The are compressed into a small region of space. The rarefactions are regions of low pressure, where the rarefactions are regions of low pressure, where the air molecules are spread apart. This alternating air molecules are spread apart. This alternating pattern of compressions and rarefactions is known as pattern of compressions and rarefactions is known as

a sound wavea sound wave. .

Sound From a StringA sound wave is produced by a vibrating object. As a guitar string vibrates, it sets surrounding air molecules into vibrational motion. The frequency at which these air molecules vibrate is equal to the frequency of vibration of the guitar string.

Reaction of the Air

The back and forth vibrations of the surrounding air molecules creates a pressure wave which travels outward from its source. This pressure wave consists of compressions and rarefactions.

Sound Wave

• The compressions are regions of high pressure, where the air molecules are compressed into a small region of space.

• The rarefactions are regions of low pressure, where the air molecules are spread apart.

• This alternating pattern of compressions and rarefactions is known as a sound wave.

Pitch

How high or low a sound is, related to the How high or low a sound is, related to the frequency of the sound. frequency of the sound.

Higher pitches have higher frequency Higher pitches have higher frequency waves. waves.

Decaying Sound

• Frequency (F)

• Initial Amplitude (Amax)

• Halving Time (T½)

Reverberation

Ultrasound

Very high frequency sound waves, Very high frequency sound waves, higher than we can hear. higher than we can hear.

Used in medicine in imaging and to Used in medicine in imaging and to destroy kidney stones in the bladderdestroy kidney stones in the bladder

Applications of Sound

SonarSonar Ultrasound AnalysisUltrasound Analysis Bats EcholocationBats Echolocation Insect Repellant/Dog WhistleInsect Repellant/Dog Whistle

Musical Scale 8 notes in the 8 notes in the

scale, scale, key is the key is the starting note starting note Key of C has Key of C has CDEFGABCDEFGAB

Notes repeat in Notes repeat in octaves. octaves.

One octave is One octave is double the double the frequency of the frequency of the one below.one below.

Pure tones, complex tones, and noise.

Beats

Waves close in frequency sometimes Waves close in frequency sometimes constructively interfere, causing a constructively interfere, causing a sudden loudness. sudden loudness.

E.G. sound of 500 hz and 502 hz, 2 hz E.G. sound of 500 hz and 502 hz, 2 hz is the difference or beat frequency, is the difference or beat frequency, 502 –500 = 2502 –500 = 2

Two times per second they would Two times per second they would interfere constructively.interfere constructively.

Musical Instruments

Recognize some differences in the Recognize some differences in the ways various musical instruments ways various musical instruments produce sound.produce sound. wind instruments: blow reed vibrateswind instruments: blow reed vibrates percussion: stike and they vibratepercussion: stike and they vibrate strings: pluck or bow and they vibratestrings: pluck or bow and they vibrate

Harmonics

Harmonics are sounds emitted in simple Harmonics are sounds emitted in simple ratios of the main or fundamental frequencyratios of the main or fundamental frequency

First Harmonic or fundamental = fFirst Harmonic or fundamental = f Second H = 2fSecond H = 2f Third H= 3f, etc.Third H= 3f, etc.

Harmonic Diagrams

1st

2nd

Sum

Standing Wave Demo

http://id.mind.net/~zona/mstm/physics/http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/waves/standingWaves/standingWaves1/StandingWaves1.htmlStandingWaves1.html

Superposition of Waves

Problem on Harmonics

If a sound of A has 220 Hz, what are the If a sound of A has 220 Hz, what are the first and third harmonics?first and third harmonics?

1st H = f = 1 x 220 = 220 Hz1st H = f = 1 x 220 = 220 Hz 22ndnd H = 2 x f, H = 2 x f, third = 3 x f = 3 x 220 = 660Hzthird = 3 x f = 3 x 220 = 660Hz

Loudness and Decibels

A bel is a rating of the power of 10 of the A bel is a rating of the power of 10 of the amplitude of a wave. E.g. 10, vs 100, = 1 amplitude of a wave. E.g. 10, vs 100, = 1 bel more (10bel more (1011 vs. 10 vs. 1022 ) which is 10 decibels ) which is 10 decibels

Related to intensity of the sound. Closest Related to intensity of the sound. Closest measurement is the decibel (.1 bel)measurement is the decibel (.1 bel)

Minimum difference in intensity we can Minimum difference in intensity we can hear is 1 db, to sound louderhear is 1 db, to sound louder

Decibel Ratings

120 db is the threshold of pain120 db is the threshold of pain 2 identical sounds are 3 db higher than the single 2 identical sounds are 3 db higher than the single

sound. sound. It takes 10 identical sounds to sound twice as loud, It takes 10 identical sounds to sound twice as loud,

which is a change of 10 db.which is a change of 10 db. This is cumulative, 100 db sounds 4x as loud as 80 db.This is cumulative, 100 db sounds 4x as loud as 80 db.

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