Physics 1251 The Science and Technology of Musical Sound Unit 1 Session 3 Sound Waves Unit 1 Session 3 Sound Waves

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Unit 1Unit 1

Session 3 Session 3

Sound WavesSound Waves

Unit 1Unit 1

Session 3 Session 3

Sound WavesSound Waves

Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves

Foolscap Quiz: Foolscap Quiz: If a person can only distinguish an If a person can only distinguish an echo if it occurs more than 0.100 sec echo if it occurs more than 0.100 sec after the initial sound, then how far after the initial sound, then how far from a wall must he be to hear a from a wall must he be to hear a distinct echo of his clapping hands?distinct echo of his clapping hands?

Round trip time = 0.1 sec. Round trip time = 0.1 sec. One way = (0.1)/2 sec= 0.05 secOne way = (0.1)/2 sec= 0.05 sec

d = vd = v‧ t = (343 m/s)‧ (0.05 sec) = 17.1 m ~ 57 ‧ t = (343 m/s)‧ (0.05 sec) = 17.1 m ~ 57 feetfeet


11′ Lecture:′ Lecture:• Sound is a pressure/displacement wave Sound is a pressure/displacement wave

that propagates in air with a velocity that that propagates in air with a velocity that increases by 0.6 m/s for every degree C increases by 0.6 m/s for every degree C above room temperature.above room temperature.

• v = 343 m/s + 0.6 (T-20 C)v = 343 m/s + 0.6 (T-20 C)• Waves are characterized by frequency Waves are characterized by frequency f,f,

period P, wavelength period P, wavelength λλ, , velocity v. velocity v.• f = f = 1/ P 1/ P • f f ⋅ ⋅ λλ = = vv


80/2080/20Pressure = Force per unit Pressure = Force per unit AreaArea

p = F /Ap = F /A


80/2080/20The unit of pressure in SI units is The unit of pressure in SI units is the the

Pascal [Pa] = 1 Newton/ mPascal [Pa] = 1 Newton/ m22

1 Newton 1 Newton forceforce

1 square meter 1 square meter areaarea

1 Pascal 1 Pascal pressure:pressure:


80/2080/20Standard atmosphere = 1.0 Standard atmosphere = 1.0 atm atm

=101 kPa=101 kPa

=14.7 psi=14.7 psi

Tire Tire pressurepressure

A few 100 A few 100 kPakPa

Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves

Which applies Which applies

the greatest the greatest

pressure on pressure on

their foot?their foot?

Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound WavesForce = 200 lb = Force = 200 lb = 891 N891 N

Force = 4,000 lb = Force = 4,000 lb = 17,800 17,800 NN

Force = 100 lb = Force = 100 lb = 445 N445 N

Foot Area = 36.2 inFoot Area = 36.2 in22 = = 0.023 m0.023 m22

Foot Area = 43.5 inFoot Area = 43.5 in22 = = 0.028 m0.028 m22

Foot Area = 12.7 inFoot Area = 12.7 in22 = = .0082 m.0082 m22

p = F/A =200/(2 x 36.2) = 2.8 psip = F/A =200/(2 x 36.2) = 2.8 psip = 891/(2 x 0.023) = p = 891/(2 x 0.023) = 19 kPa19 kPa

p = F/A =4000/(4 x 43.5) = 23. psip = F/A =4000/(4 x 43.5) = 23. psip = 17800/(4 x 0.028) = p = 17800/(4 x 0.028) = 159 kPa159 kPa

p = F/A =100/(2 x 12.7) = 3.9 psip = F/A =100/(2 x 12.7) = 3.9 psip = 445/(2 x 0.0082) = p = 445/(2 x 0.0082) = 27 kPa27 kPa


Force = 100 lb = Force = 100 lb = 445 N445 NHeel Area = 0.16 inHeel Area = 0.16 in22 = = .0001 m.0001 m22p = F/A =100/(2 x 0.16) = 313. psip = F/A =100/(2 x 0.16) = 313. psip = 445/(2 x 0.0001) = p = 445/(2 x 0.0001) = 2200. kPa2200. kPa

p = p = 19 kPa19 kPa

p = p = 159 kPa159 kPa

p = p = 27 kPa27 kPa


The Mysterious Swami SeatThe Mysterious Swami Seat


80/2080/20Pressure = Force per unit Pressure = Force per unit AreaArea

p = F /Ap = F /A

Same ForceSame Force

Different AreaDifferent Area

∴∴Different Different PressurePressure


80/2080/20Sound is a pressure wave.Sound is a pressure wave.


Talking About of Talking About of WavesWaves


80/2080/20FrequencyFrequency f f is the number of is the number of cycles or pulses per unit time.cycles or pulses per unit time.

[ [ f ] f ] = Hertz = Hz = 1/sec= Hertz = Hz = 1/sec


80/2080/20PeriodPeriod is the is the timetime it takes to it takes to make one cycle, oscillation or make one cycle, oscillation or

pulse.pulse.

[P] = second[P] = second

80/20 80/20 P = 1/ P = 1/ ff


80/2080/20WavelengthWavelength λλ is the is the distancedistance from one point on a wave to a from one point on a wave to a corresponding point (point of corresponding point (point of the same phase) on the next the same phase) on the next cycle.cycle.

[[λλ]= m]= m

λλ

λλ

λλ


� � λ λ ��WavelengthWavelength

V V


Chain of Inference:Chain of Inference:1. The distance a wave moves in one 1. The distance a wave moves in one

cycle = cycle = λλ2. Time for one cycle = period P2. Time for one cycle = period P

3. v = distance moved / time to move3. v = distance moved / time to move

4. Therefore, v = 4. Therefore, v = λλ / P = / P = λλ ⋅ ⋅ ff

Physics 1251Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves

80/2080/20 Fact: Fact:

v = v = λλ ⋅ ⋅ ff

Always!Always!

Physics 1251Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves

80/2080/20 Fact: Fact:

Sound travels faster in warm air than in Sound travels faster in warm air than in cold.cold.


Most accurate relationship of sound Most accurate relationship of sound velocity on temperature isvelocity on temperature is

v = 343 v = 343 √{(T +293)/293} m/s√{(T +293)/293} m/s


80/2080/20 Most convenient approximation of the Most convenient approximation of the relationship of sound velocity and relationship of sound velocity and

temperature temperature

v = 343 +0.6v = 343 +0.6(T - 20 C) m/s(T - 20 C) m/s

What is the speed of sound on a hot day What is the speed of sound on a hot day when it is 40 C?when it is 40 C? v = 343 + 0.6 (40-20) = 343 + 0.6 (20) = 343 + v = 343 + 0.6 (40-20) = 343 + 0.6 (20) = 343 +

12 = 355 m/s12 = 355 m/s


Velocity of Sound vs Temperature

0

100

200

300

400

500

600

700

-300 -200 -100 0 100 200 300 400 500 600

Temperature (C)

Ve

loc

ity

of

So

un

d

(m/s

)

Exact formula

Approximate formula


© Pat Brady and United Media© Pat Brady and United Media


© Pat Brady and United © Pat Brady and United MediaMedia


Summary:Summary:• p = F / Ap = F / A• Standard atmospheric pressure = 101 Standard atmospheric pressure = 101

kPakPa• Frequency = number of cycles per Frequency = number of cycles per

secondsecond• Hz = Hertz = cycle/secondHz = Hertz = cycle/second• Period P = 1/ Period P = 1/ ff• v = v = λλ ⋅ ⋅ ff • v = 343 + 0.6 (T – 20 C) m/sv = 343 + 0.6 (T – 20 C) m/s


Credits:Credits:• Photographs & GraphicsPhotographs & Graphics

• Ross Clarke-JonesRoss Clarke-Jones

www.www.• ““Rose is Rose” by Pat BradyRose is Rose” by Pat Brady

© United Media© United Media

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Physics 1251 The Science and Technology of Musical Sound Unit 1 Session 3 Sound Waves Unit 1 Session 3 Sound Waves