Physics 1251 The Science and Technology of Musical Sound

1. Physics 1251The Science and Technology of Musical Sound Unit 2 Session 17 MWF The Wave Properties: Propagation and Addition

2. Physics 1251 Unit 2 Session 17 Propagation and Addition Foolscap Quiz: A jet airplane flies over you at an altitude of 10 km. If the Sound Intensity Level 10 meters from the engine is 120 dB ( 1 W/m2), what is the SIL ( or intensity) you hear? Answer: 60 dB. (1 x 10 -6 W/m2). SIL = SIL0 – 20 Log (d/d0 ) SIL = 120 dB – 20 Log(10 000/10) = 120 – 20 x 3 = 120 – 60 = 60 dB

3. Physics 1251 Unit 2 Session 17 Propagation and Addition 1′ Lecture: • Wave motion is characterized by • Reflection • Refraction • Diffraction • Doppler Shift • Beats • Interference The Reflective Ref Differed Dopily, Beating Interference.

4. Physics 1251 Unit 2 Session 17 Propagation and Addition When the surface is smooth we have “specular” (mirror-like) reflection. Reflection Smooth Surface Roughness ≲ λ

5. Physics 1251 Unit 2 Session 17 Propagation and Addition Examples of Acoustic Reflection: • Echoes • Band Shells • Reverberations

6. Physics 1251 Unit 2 Session 17 Propagation and Addition What happens when a wave “hits” a change in the medium? Reflection Θin = Θout Θout Θout Θin Θin Transmission Medium 1 Medium 2

7. Physics 1251 Unit 2 Session 17 Propagation and Addition What if the surface is rough? Diffuse Reflection Rough Surface Roughness > λ

8. Physics 1251 Unit 2 Session 17 Propagation and Addition Reflection: 80/20Reflection, a “bouncing back,” occurs whenever there is an abrupt change in the medium.

9. Physics 1251 Unit 2 Session 17 Propagation and Addition Refraction occurs when a wave “enters” a medium that has a different velocity. Refraction V1 < V2

10. Physics 1251 Unit 2 Session 17 Propagation and Addition In the second medium the wavefront “races ahead,” changing the direction. Refraction V1 V2

11. Physics 1251 Unit 2 Session 17 Propagation and Addition Refraction: When a band marches around a corner the marchers on the outside must march faster than those on the inside.

12. Slower Faster Physics 1251 Unit 2 Session 17 Propagation and Addition Refraction Parade Analogy

13. Physics 1251 Unit 2 Session 17 Propagation and Addition Thought question: What happens to a sound wave when the wind is blowing? • If there is a “wind shear,” • then refraction will occur.

14. Physics 1251 Unit 2 Session 17 Propagation and Addition Wind Speed Refraction velocity varies along wavefront

15. Physics 1251 Unit 2 Session 17 Propagation and Addition The Mystery of the “Silent Lightening”

16. Physics 1251 Unit 2 Session 17 Propagation and Addition v = 343 + 0.6 (T- 20C) Cold aloft v - slower Refraction: velocity varies with temperature v - faster Warm below silence

17. Physics 1251 Unit 2 Session 17 Propagation and Addition Refraction: 80/20Refraction, a “bending aside,” occurs whenever there is a change in velocity along the wavefront.

18. Physics 1251 Unit 2 Session 17 Propagation and Addition Diffraction What happens when a wave “is partially obstructed?

19. Physics 1251 Unit 2 Session 17 Propagation and Addition Diffraction: 80/20Diffraction, a “bending around” obstacles because every point on a wave is a source; waves cannot terminate abruptly.

20. Physics 1251 Unit 2 Session 17 Propagation and Addition 80/20Huygens Principle: every point on the wave is the source of a new (spherical) “wavelet.”

21. Physics 1251 Unit 2 Session 17 Propagation and Addition How can you hear someone who is around a corner? Diffraction

22. Physics 1251 Unit 2 Session 17 Propagation and Addition Doppler Shift: Moving source Lower f Higher f fobserver = fsource [v + vobserver] / [v – vsource]

23. Physics 1251 Unit 2 Session 17 Propagation and Addition Doppler Shift: 80/20The Doppler shift is the change in the frequency of a source fsource observed fobserved due to the relative velocity of the source vsource , observer vobserver ,where the velocity of sound in the still medium is v.f observed= f source ‧ [v + vobserver] / [v - vsource]

24. Physics 1251 Unit 2 Session 17 Propagation and Addition Addition of Waves: 80/20Coherent addition is the addition of the amplitudes of waves of the same frequency.The intensity then is proportional to the square of the the combined amplitude. Icoherent = (a1 + a2 )2 = a12 + a22 + 2a1a2 80/20Incoherent addition of waves is equal to the sum of their independent intensities if they are not within the critical bandwidth. Iincoherent = a12 + a22

25. Physics 1251 Unit 2 Session 17 Propagation and Addition Beats 80/20Beats are a modulation of intensity of due to the coherent addition of two sound waves whose frequency lie with a critical band width of each other.

26. Physics 1251 Unit 2 Session 17 Propagation and Addition Beat Frequency 80/20Two tones of frequency f1 and f2 sound like one tone of mean frequency f mean= (f1 +f 2)/2 that beats at a beat frequency of f beat= f1 – f2 .

27. Physics 1251 Unit 2 Session 17 Propagation and Addition Beats f1 f2 In phase Out of phase fmean fbeat

28. Physics 1251 Unit 2 Session 17 Propagation and Addition Tuning a Guitar by Beats 80/20Two tones of frequency f1 and f2 sound like one tone of mean frequency f mean= (f1 +f 2)/2 that beats at a beat frequency of f beat= f1 – f2 .

29. Physics 1251 Unit 2 Session 17 Propagation and Addition Interference: 80/20Interference is the coherent addition of waves at various points in space that leads to modulation of the intensity in space.

30. Physics 1251 Unit 2 Session 17 Propagation and Addition Interference Constructive Destructive Softer Louder

31. Physics 1251 Unit 2 Session 17 Propagation and Addition Summary • Reflection is the return of a wave from a change in a medium. • Refraction is bending of the wave due to velocity variation along the wavefront. • Diffraction is the bending of the wave around obstacles because of Huygen’s Principle. • Doppler Shift is the change in frequency due to the relative motion.

32. Physics 1251 Unit 2 Session 17 Propagation and Addition Summary • Beats are intensity modulations in time due to coherent addition of waves of near equal frequency. • Interference is spatial modulation of intensity due to the coherent addition of nearly equal frequency waves at different points in space.