Physics 1251 The Science and Technology of Musical Sound

1. Physics 1251The Science and Technology of Musical Sound Unit 2 Session 16 MWF The Wave Properties: Propagation

2. 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!

3. Physics 1251 Unit 2 Session 16 Wave Properties: Propagation Georg Phillip Telemann Sonata IV in E minor Recorded by Ron DiIulio (UNT September 2001)

4. Physics 1251 Unit 2 Session 16 Wave Properties: Propagation Georg Phillip Telemann Sonata IV in E minor Notice the “difference tones”

5. 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

6. 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 )

7. 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.

8. 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

9. 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

10. 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.

11. 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

12. 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

13. 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)

14. 10 Log(I/Ithreshold) – 10 Log(I0 /Ithreshold) = 20 Log((r0 /r)) SIL – SIL0 = -20 Log(r/r0 ) 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)

15. 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

16. 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)