Physics 1251 The Science and Technology of Musical Sound

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Physics 1251The Science and Technology of
Musical Sound

• Unit 2
• Session 16 MWF
• The Wave Properties Propagation

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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Foolscap Quiz
• What is frequency of the pitch that a person
  will perceive, if he hears the harmonics in the
  vibration recipe 350 Hz, 525 Hz, 700 Hz and 875
  Hz?

Answer 175 Hz (F3), fundamental of series 350
Hz (F4), 525 Hz (C5), 700 Hz (F5) and 875 Hz
(A5). We hear the difference frequencies
(525-350) (700-525) (875-350) 175 Hz!
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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Georg Phillip Telemann
• Sonata IV in E minor
• Recorded by Ron DiIulio (UNT September 2001)

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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Georg Phillip Telemann
• Sonata IV in E minor
• Notice the difference tones

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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• 1' Lecture
• The intensity of sound decreases with the square
  of the inverse of the distance from the source in
  an open area.
• I / I0 (r0 /r) 2

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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• 1' Lecture
• The Sound Intensity Level (SIL) diminishes with
  distance thus
• SIL SIL0 20 Log (r / r0 )

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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Thought question
• What happens to a sound wave as it propagates or
  travels?

• Wave is absorbed.

• not much 10 dB/km

• Wave spreads out.

• depends of geometry.

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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• The intensity of a spherical sound wave decreases
  as the distance from the source increases.
  Inverse

d m I W/m2
1.0 1.0
12 /12 12/2 2 12 /3 2 12 /4 2 12 /5 2 As
1/r 2
2.0 0.25
3.0 0.11
4.0 0.068
5.0 0.040
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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Intensity is Power per Unit Area
• Why does intensity
• diminish as 1/r 2?Area 2/3p ? r 2
• I Power/Area
• I I0 (A0 /A)
• I I0 (r0 / r ) 2

A ?p r 2
r
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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Demonstration of Inverse Square Law

I1 I1 ? (r1 /r2) 2 I1 ? (r1
/r3)2
Source
r1
r2
r3
The fraction of the sound energy that enters the
ear decreases as the ratio of the inverse of the
square of the distance because the fractional
area decreases as 1/r 2.
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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• 80/20Inverse Square Law
• The intensity of sound (originating from a point
  source in an open environment) diminishes as the
  square of the inverse ratio of the distances from
  a source.
• I / I0 (r0 /r) 2

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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Practice
• The sound intensity is 1.0 x10 -9 W/m2 at a
  distance of 3.0 m from a speaker. What is the
  intensity 20 m away?

I2 / I1 ( r1 /r2 ) 2 I2 / (1 .0 x10-9
W/m2) ( 3.0 m / 20 m ) 2 I2 (1 .0 x10-9
W/m2) (.0225) 2.25 x10 -11 W/m2
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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• 80/20Inverse Square Law
• The Sound Intensity Level (SIL) decreases by 20
  dB for every 10x increase in distance.

SIL SIL0 20 Log (r / r0)
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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• 80/20Inverse Square Law
• If I / I0 (r0 /r) 2

Then 10 Log (I / I0 ) 10 Log((r0 /r) 2)
10 Log(I/Ithreshold) 10 Log(I0 /Ithreshold)
20 Log((r0 /r))
SIL SIL0 -20 Log(r/r0 )
SIL SIL0 20 Log (r / r0)
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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Practice
• The sound intensity level of the professors
  lecture is 80 dB on the front row of the
  classroom, 3 m from the his mouth. What is the
  SIL at the back row if it is 6 m away and there
  are no reflections?

SIL SIL0 20 dB Log ( r /r0 ) SIL 80 dB
20 dB Log ( 6 m/3 m) 74 dB
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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Summary
• The intensity of sound decreases with the square
  of the inverse of the distance from the source in
  an open area.
• I / I0 ( r /r0 ) 2
• The Sound Intensity Level diminishes with
  distance thus
• SIL SIL0 20 Log (r / r0)