physics 1251 the science and technology of musical sound unit 1 session 3 sound waves unit 1 session...
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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
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
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
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
80/2080/20Pressure = Force per unit Pressure = Force per unit AreaArea
p = F /Ap = F /A
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
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:
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
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
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
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
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
The Mysterious Swami SeatThe Mysterious Swami Seat
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
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
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
80/2080/20Sound is a pressure wave.Sound is a pressure wave.
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
Talking About of Talking About of WavesWaves
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
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
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
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
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
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
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
� � λ λ ��WavelengthWavelength
V V
Physics 1251 Physics 1251 Unit 1 Session 3 Sound WavesUnit 1 Session 3 Sound Waves
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.
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
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
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
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
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
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
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
© Pat Brady and United Media© Pat Brady and United Media
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
© Pat Brady and United © Pat Brady and United MediaMedia
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
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
Physics 1251 Unit 1 Session 3 Sound WavesPhysics 1251 Unit 1 Session 3 Sound Waves
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