Transcript Physics 1251 The Science and Technology of Musical Sound

Physics 1251
The Science and Technology
of Musical Sound
Unit 2
Session 16 MWF
The Wave Properties:
Propagation
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!
Physics 1251
Unit 2 Session 16
Wave Properties: Propagation
Georg Phillip Telemann
Sonata IV in E minor
Recorded by Ron DiIulio (UNT September 2001)
Physics 1251
Unit 2 Session 16
Wave Properties: Propagation
Georg Phillip Telemann
Sonata IV in E minor
Notice the “difference tones”
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
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 )
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.
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]
1.0
I [W/m2]
1.0
=12 /12
2.0
0.25 =12/2 2
3.0
0.11
4.0
0.068 = 12 /4 2
5.0
0.040 = 12 /5 2
=12 /3 2
As 1/r 2
Physics 1251
Unit 2 Session 16
Wave Properties: Propagation
Intensity is Power per Unit Area
Why does intensity
diminish as 1/r 2?
Area = 2/3π ‧ r 2
I = Power/Area
I = I0 (A0 /A)
I= I0 (r0 / r ) 2
A = ⅔π r 2
r
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.
Physics 1251
80/20Inverse
Unit 2 Session 16
Wave Properties: Propagation
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
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
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)
Physics 1251
80/20Inverse
Unit 2 Session 16
Wave Properties: Propagation
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)
Physics 1251
Unit 2 Session 16
Wave Properties: Propagation
Practice:
The sound intensity level of the professor’s
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
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)