SoundSound

Chapter 13Chapter 13

Sound WavesSound Waves

Sound waves are areas Sound waves are areas of alternating high and of alternating high and low molecular densities.low molecular densities. LongitudinalLongitudinal Caused by vibrationsCaused by vibrations

Compression-areas of Compression-areas of high molecular densityhigh molecular density

Rarefactions-areas of Rarefactions-areas of low molecular densitylow molecular density

Speed of SoundSpeed of Sound

The speed of sound depends on the The speed of sound depends on the medium in which it propagates.medium in which it propagates. Solids Solids LiquidsLiquids GasesGases HotHot ColdCold (Fast to Slow)(Fast to Slow)

Tvair 6.0331

Human HearingHuman Hearing

Audible SoundsAudible Sounds Humans can hear frequencies (known as Humans can hear frequencies (known as

pitch) between 20 Hz and 20,000 Hzpitch) between 20 Hz and 20,000 Hz Frequencies higher than we can hear…Frequencies higher than we can hear…

UltrasonicUltrasonic

Frequencies lower than we can hear…Frequencies lower than we can hear… infrasonicinfrasonic

Sound CharacteristicsSound Characteristics

Pitch-results from differences in frequencyPitch-results from differences in frequency The higher the frequency, the higher the pitchThe higher the frequency, the higher the pitch Don’t directly observe wavelengthDon’t directly observe wavelength Infrasonic and UltrasonicInfrasonic and Ultrasonic

Loudness-results from amplitudeLoudness-results from amplitude Logarithmic relationship between intensity and Logarithmic relationship between intensity and

perceived loudness.perceived loudness. Increasing intensity by 10 times only results in a Increasing intensity by 10 times only results in a

doubling of perceived loudness.doubling of perceived loudness.

IntensityIntensity

Area

PowerIntensity

Rate at which energy flowsRate at which energy flows Inverse square relationshipInverse square relationship Units of W/mUnits of W/m22

We will assume the sound spreads in all We will assume the sound spreads in all directions equally so the area we are dealing directions equally so the area we are dealing with is the surface area of a sphere (4with is the surface area of a sphere (4ππrr22).).

Intensity and Human Intensity and Human HearingHearing

Intensity ranges:Intensity ranges: Threshold of Hearing to Threshold of PainThreshold of Hearing to Threshold of Pain 1.0 x 101.0 x 10-12-12 WW/m/m22 to 1 to 1 WW/m/m22

This is a large range:This is a large range: Logarithmic scale compresses this rangeLogarithmic scale compresses this range Use Decibel levelsUse Decibel levels

The Decibel ScaleThe Decibel Scale

Hearing damage Hearing damage starts at 85dBstarts at 85dB

For each 10dB step, For each 10dB step, the intensity the intensity increases by 10 increases by 10 times and the times and the perceived loudness perceived loudness increases by 2 times.increases by 2 times.

ExamplesExamples1.1. Calculate the intensity of the sound waves from an Calculate the intensity of the sound waves from an

electric guitar’s amplifier at a distance of 5.0 m when its electric guitar’s amplifier at a distance of 5.0 m when its power output is equal to each of the following values:power output is equal to each of the following values:

a.a. 0.25 W0.25 W

b.b. 0.50 W0.50 W

c.c. 2.0 W2.0 W

a.a. If the intensity of a person’s voice is 4.6 x 10If the intensity of a person’s voice is 4.6 x 10-7-7 WW/m/m22 at a at a distance of 2.0 m, how much sound power does that distance of 2.0 m, how much sound power does that person generate?person generate?

b.b. The power output of a tuba is 0.35 W. At what distance The power output of a tuba is 0.35 W. At what distance is the sound intensity of the tuba 1.2 x 10is the sound intensity of the tuba 1.2 x 10-3-3 WW/m/m22??

The Doppler EffectThe Doppler Effect

The shift in perceived frequency of a wave due to The shift in perceived frequency of a wave due to relative motion between the source and the observer.relative motion between the source and the observer.

Observable in both sound (pitch) and light (red and Observable in both sound (pitch) and light (red and blue shifts)blue shifts)

As the sound approaches - higher fAs the sound approaches - higher f As sound leaves - lower fAs sound leaves - lower f Occurs as either listener or source is movingOccurs as either listener or source is moving

Forced Vibrations and Forced Vibrations and Natural FrequencyNatural Frequency

Forced Vibration – a vibration that occurs Forced Vibration – a vibration that occurs when a periodic force causes an object to when a periodic force causes an object to vibrate at a particular frequencyvibrate at a particular frequency SingingSinging

Natural Frequency – the frequency an Natural Frequency – the frequency an object will vibrate at when given a one object will vibrate at when given a one time forcetime force Depends on shape and material of objectDepends on shape and material of object

ResonanceResonance The amplified wave The amplified wave

that occurs when a that occurs when a forced vibration on an forced vibration on an object matches the object matches the natural frequency of natural frequency of the object.the object.

Makes the wave Makes the wave progressively larger.progressively larger.

Swing set exampleSwing set example

MusicMusic

Different notes have different Different notes have different mathematical relationships mathematical relationships between their frequencies.between their frequencies.

Specific frequency Specific frequency combinations are considered combinations are considered pleasant (harmony) and others pleasant (harmony) and others unpleasant (dissonance).unpleasant (dissonance). 2:1 = Octave (C to the next C)2:1 = Octave (C to the next C) 5:4 = Major Third (C to E)5:4 = Major Third (C to E) 4:3 = Perfect Forth (C to F)4:3 = Perfect Forth (C to F) 3:2 = Perfect Fifth (C to G)3:2 = Perfect Fifth (C to G)

InstrumentsInstruments

The sound produced by the vibration of a The sound produced by the vibration of a piece of the instrument (string, reed, lips) piece of the instrument (string, reed, lips) is amplified and shaped through is amplified and shaped through resonance by the rest of the instrument.resonance by the rest of the instrument.

Standing waves are produced within the Standing waves are produced within the instrument at certain frequencies instrument at certain frequencies depending on either the properties of the depending on either the properties of the string or the shape and size of the string or the shape and size of the instrument.instrument.

StringsStrings

Physically, wavelength is Physically, wavelength is restricted to certain values.restricted to certain values.

To change those values, the To change those values, the length of the string needs to length of the string needs to be changed (different keys be changed (different keys on a piano, different finger on a piano, different finger placements on a guitar)placements on a guitar)

The longest wavelength on The longest wavelength on the string is the sound you the string is the sound you hear as the note being hear as the note being played and is called the played and is called the fundamental or first fundamental or first harmonic.harmonic.

WavelengthsWavelengths

The higher frequency vibrations are played The higher frequency vibrations are played simultaneously and are called overtones. Therefore, simultaneously and are called overtones. Therefore, the next longest wavelength will be the second the next longest wavelength will be the second harmonic or first overtone.harmonic or first overtone.

L

L

21

121

2LL

L

32

3

323

L

L

21

4

42

FrequenciesFrequencies

Since all of the waves are on the same medium and Since all of the waves are on the same medium and travel at the same speed, there will be a pattern to the travel at the same speed, there will be a pattern to the frequency as well as the wavelength.frequency as well as the wavelength.

n

nn

nn

fL

nv

nLv

fv

fv

22

n

Ln

2

1nffn

L

vf

21

Closed PipeClosed Pipe Node on one end, antinode on the other.Node on one end, antinode on the other. Diagrams help with determining wavelength Diagrams help with determining wavelength

pattern.pattern.

Wavelengths and Wavelengths and FrequenciesFrequencies

n

Ln

4

354

345

234

243

1141 4

LL

LL

LL

1

44

nff

L

nv

nLv

f

vf

fv

n

n

nn

nn

Where n=1, 3, 5…Where n=1, 3, 5… Closed pipes have Closed pipes have

only odd harmonicsonly odd harmonics

Open PipesOpen Pipes The same as the closed pipe, however there is The same as the closed pipe, however there is

an anti-node at each end for molecular an anti-node at each end for molecular movement and a node at each end for movement and a node at each end for pressure variance.pressure variance.

Wavelengths and Wavelengths and FrequenciesFrequencies

n

Ln

2

332

323

2

1121 2

LL

L

LL

1

22

nff

L

nv

nLv

f

vf

fv

n

n

nn

nn

BeatsBeats

Beats are a result of two waves Beats are a result of two waves with close, but not identical with close, but not identical frequencies.frequencies.

A pattern of constructive and A pattern of constructive and destructive interference forms destructive interference forms creating a warbling sound.creating a warbling sound.

Useful for tuning instruments.Useful for tuning instruments. Beat frequency is equal to the Beat frequency is equal to the

difference between the two difference between the two component frequencies.component frequencies.

TimbreTimbre The unique combination of The unique combination of

intensities of fundamental intensities of fundamental and overtone frequencies and overtone frequencies that makes instruments that makes instruments sound different when playing sound different when playing the same note.the same note.

Trumpet

Flute

Cello

ExamplesExamples1.1. What is the fundamental frequency of a 0.2 m long organ pipe that is What is the fundamental frequency of a 0.2 m long organ pipe that is

closed at one end, when the speed of sound in the pipe is 352 m/s?closed at one end, when the speed of sound in the pipe is 352 m/s?

2.2. A flute is an open pipe. The length is the flute is approximately 66.0 A flute is an open pipe. The length is the flute is approximately 66.0 cm. What are the first three harmonics of a flute when all keys are cm. What are the first three harmonics of a flute when all keys are closed, making the length of air equal to the length of the flute? Use closed, making the length of air equal to the length of the flute? Use 340 m/s for the speed of sound.340 m/s for the speed of sound.

3.3. What is the fundamental frequency of a guitar string when the speed What is the fundamental frequency of a guitar string when the speed of waves on the string is 115 m/s and the effective string lengths are of waves on the string is 115 m/s and the effective string lengths are as follows:as follows:

a.a. 70.0 cm70.0 cm

b.b. 50.0 cm50.0 cm

c.c. 40.0 cm40.0 cm

4.4. A violin string that is 50.0 cm in length has a fundamental frequency A violin string that is 50.0 cm in length has a fundamental frequency of 440 Hz. What is the speed of the waves on this string?of 440 Hz. What is the speed of the waves on this string?