1. Sound Intensity Energy flux at your eardrums § 16.3

2. Sound Intensity I = (Power output)/(Area) = (Force) (Displacement velocity)/(Area) = (Force/Area) (Displacement velocity) = (Pressure) (Displacement velocity) = p(x,t) v y (x,t)

3. Intensity and Distance Inverse-square law: Source transmits power P At distance R, energy is spread over area A = 4  R 2 Intensity at distance R is P/A I R = P 4R24R2

4. Sound Intensity Level Decibel scale Reference intensity I 0 = 10 –12 W/m 2 Audibility threshold at 1000 Hz  = (10 dB) log 10 I0I0 I A 10-dB increase in intensity level represents a factor-of-10 increase in sound intensity

5. Decibel Differences  2 –  1 = (10 dB) log 10 I1I1 I2I2 = (10 dB) log 10 R12R12 R22R22 = (20 dB) log 10 R1R1 R2R2  = (10 dB) log 10 I0I0 I

6. Example Problem 30 m from an outdoor concert stage, the sound intensity level is 80 dB. What is the sound intensity level 40 m from the stage?  2 –  1 = (20 dB) log 10 (R 1 /R 2 )  2 =  1 + (20 dB) log 10 (R 1 /R 2 ) = 80 dB + (20 dB) log 10 (30/40) = 80 dB + (20 dB) (–0.125) = 80 dB – 2.50 dB = 77.5 dB

7. Longitudinal Waves § 16.1

8. Group Poll For any wave/oscillation: –What is the particle acceleration when the particle speed is greatest? A. ±Maximum.B. Zero. C. ? –What is the particle speed when the particle acceleration is greatest? A. Maximum.B. Zero. C. ?

9. Longitudinal Waves 0 1/8 T 2/8 T 3/8 T 4/8 T 5/8 T 6/8 T 7/8 T Where are crests and troughs? Which way is acceleration?

10. Board Work Draw several cycles of a longitudinal wave train. –What force accelerates the particles? –Identify where pressure is high or low. –Identify the acceleration directions at different positions along a phase.

11. Group Poll For a sound wave: –What is the pressure excursion where the particle acceleration is greatest? A. Maximum.B. Zero. C. ? –What is the particle acceleration where the pressure excursion is greatest? A. Maximum.B. Zero. C. ?

12. End Result Pressure is 90° out of phase with displacement Pressure is greatest when forward velocity is greatest Pressure is least when backward velocity is greatest

13. Combining Waves interference § 15.6–15.8, 16.6

14. Principle of Superposition Where waves meet, the displacement is the sum of the displacements from the individual waves. result 0 –3 3

15. Interference Constructive: Sum of waves has increased amplitude Destructive: Sum of waves has decreased amplitude Two-wave simulation

16. Beats Interference of similar frequencies § 16.7

17. Beats Waves of similar frequency combine to give alternating times of constructive and destructive interference Distinctive “waa-waa” sound with beat frequency equal to the difference in frequency of the component waves (Why?)

18. Beats Sound files Ripple tank simulator http://www.falstad.com/ripple/ http://www.falstad.com/ripple/

19. Standing Waves waves that don’t actually travel § 15.7

20. Standing Waves Sum of waves of equal amplitude and wavelength traveling in opposite directions Half-wavelength divides exactly into the available space Wave pattern has locations of minimum and maximum variation (nodes and antinodes) (standing longitudinal waves)standing longitudinal waves

21. Normal modes standing waves generalized § 15.8

22. Resonance Objects have characteristic frequencies at which standing waves are sustained Lowest frequency = fundamental Higher frequencies = overtones Sustained motion is a combination of normal modes

23. Vibrational Modes: Clamped String Source: Griffith, The Physics of Everyday Phenomena, Figure 15.13

24. Circular membrane standing waves 2-D Standing Waves Nodes are lines or curves Higher frequency  more nodes Source: Dan Russel’s pageDan Russel’s edge node onlydiameter nodecircular node

25. Resonance You’ve done this to death already § 16.4–16.5

26. Resonance Boundary conditions determine nodal positions For uniform media, resonant wavelengths and frequencies have simple relationships –Clamped strings –http://www.surendranath.org/Applets/Waves/Harmonics/HarmonicsApplet.htmlhttp://www.surendranath.org/Applets/Waves/Harmonics/HarmonicsApplet.html –Air cylinders –http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.htmlhttp://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html More complex media are more interesting –http://paws.kettering.edu/~drussell/Demos.htmlhttp://paws.kettering.edu/~drussell/Demos.html

27. Doppler Effect Distance and time § 16.8

28. Moving Source or Detector Source: successive wave fronts do not emanate from the same place Detector: successive wave fronts are not detected at the same place Simulation: http://www.astro.ubc.ca/~scharein/a311/Sim/doppler/Doppler.html http://www.astro.ubc.ca/~scharein/a311/Sim/doppler/Doppler.html

29. Moving Source or Detector Equations of Motion: Source x S = v S t Detectorx D = D + v D t n th wavefrontx n = v S (nT) + v (t – nT) Check derivation (PDF) posted on web vSvS vvDvD 0123 D

30. Differing Formulas Mine: f D = f S v – v S v – v D Book’s: f D = f S v + vSv + vS v + vDv + vD Difference: Book uses |v|, source ahead of detector Moral: Check your setup first

31. Shock Waves Energy accumulates § 16.9

32. Beyond Doppler Shift Sound waves travel from source with speed v v s = v What if source travels faster than v?

33. Sonic Boom Source: NASA, Astronomy Picture of the Day (from U.S. Navy)

34. Supersonic Shock Wave Source: Young and Freedman, University Physics, Fig. 16.35