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

2. Physics 1251Unit 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/m 2 ), what is the SIL ( or intensity) you hear? 10 km. If the Sound Intensity Level 10 meters from the engine is 120 dB ( 1 W/m 2 ), what is the SIL ( or intensity) you hear? Answer: 60 dB. (1 x 10 -6 W/m 2 ). SIL = SIL 0 – 20 Log (d /d 0 ) SIL = 120 dB – 20 Log(10 000/10) = 120 – 20 x 3 = 120 – 60 = 60 dB

3. Physics 1251Unit 2 Session 17 Propagation and Addition 1′ Lecture: Wave motion is characterized by Wave motion is characterized by ReflectionReflection RefractionRefraction DiffractionDiffraction Doppler ShiftDoppler Shift BeatsBeats InterferenceInterference The Reflective RefDifferedDopily,BeatingInterference.

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

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

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

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

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

9. Physics 1251Unit 2 Session 17 Propagation and Addition Refraction occurs when a wave “enters” a medium that has a different velocity. Refraction V 1 < V 2

10. Physics 1251Unit 2 Session 17 Propagation and Addition In the second medium the wavefront “races ahead,” changing the direction. Refraction V1V1V1V1 V2 V2 V2 V2

11. Physics 1251Unit 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. Physics 1251Unit 2 Session 17 Propagation and Addition Refraction Parade Analogy SlowerFaster

13. Physics 1251Unit 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,” If there is a “wind shear,” then refraction will occur.

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

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

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

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

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

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

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

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

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

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

24. Physics 1251Unit 2 Session 17 Propagation and Addition Addition of Waves: 80/20 Coherent 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. I coherent = (a 1 + a 2 ) 2 = a 1 2 + a 2 2 + 2a 1 a 2 80/20 Incoherent addition of waves is equal to the sum of their independent intensities if they are not within the critical bandwidth. I incoherent = a 1 2 + a 2 2

25. Physics 1251Unit 2 Session 17 Propagation and Addition Beats 80/20 Beats 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 1251Unit 2 Session 17 Propagation and Addition Beat Frequency 80/20 Two tones of frequency f 1 and f 2 sound like one tone of mean frequency f mean = (f 1 +f 2 )/2 that beats at a beat frequency of f beat = f 1 – f 2.

27. Beats f 1 f 2 Physics 1251Unit 2 Session 17 Propagation and Addition In phase Out of phase f mean f beat

28. Physics 1251Unit 2 Session 17 Propagation and Addition Tuning a Guitar by Beats 80/20 Two tones of frequency f 1 and f 2 sound like one tone of mean frequency f mean = (f 1 +f 2 )/2 that beats at a beat frequency of f beat = f 1 – f 2.

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

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

31. Summary Reflection is the return of a wave from a change in a medium. 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. 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. 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. Doppler Shift is the change in frequency due to the relative motion.

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