1. Acoustic Wave Equation

2. Acoustic Variables Pressure Density – Condensation Velocity (particle) Temperature

3. Sound Speed AirWater Steel Bulk Modulus 1.4(1.01 x 10 5) Pa 2.2 x 10 9 Pa ~2.5 x 10 11 Pa Density1.21 kg/m 3 1000 kg/m 3 ~10 4 kg/m 3 Speed 343 m/s1500 m/s 5000 m/s Please Memorize!!!

4. Necessary Differential Equations to Obtain a Wave Equation Mass Continuity Equation of State Force Equation – N2L Assumptions: homogeneous, isotropic, ideal fluid

5. Equations of State Ideal Gasses: Real Fluids:

6. Continuity Equation

7. Force Equation

8. Fluid Acceleration

9. Lagrangian and Eulerian Variables Eulerian – Fixed Moorings Lagrangian – Drifting Buoys Material, substantial or Lagrangian Derivative Eulerian Derivative Convective Term

10. Newton’s Second Law

11. Linear Continuity Equation

12. Linear Force Equation

13. Linear Wave Equation

14. Velocity Potential

15. Variation of sound speed with temperature

16. Speed of sound in water- temperature, pressure, and salinity

17. Class Sound Speed Data

18. Harmonic 1-D Plane Waves

19. Condensation and Velocity Potential

20. Specific Acoustic Impedance Mechanical Impedance For a plane wave: In general:

21. Sound Speed AirWaterSteel Bulk Modulus 1.4(1.01 x 10 5) Pa 2.2 x 10 9 Pa~2.5 x 10 11 Pa Density1.21 kg/m 3 1000 kg/m 3 ~10 4 kg/m 3 Speed 343 m/s1500 m/s5000 m/s Spec. Ac. Imp.415 Pa-s/m1.5 x 10 6 Pa-s/m 5 x 10 7 Pa-s/m Analogous to E-M wave impedance

22. Plane wave in an arbitrary direction

23. Shorthand x y z Direction Cosines Surfaces (planes) of constant phase Propagation Vector

25. k in x-y plane

26. Energy

27. Energy Density

28. Average Power and Intensity A cdt For plane waves

29. Effective Average - RMS

30. Intensity of sound Loudness – intensity of the wave. Energy transported by a wave per unit time across a unit area perpendicular to the energy flow. SourceIntensity (W/m 2 )Sound Level Jet Plane100140 Pain Threshold1120 Siren1x10 -2 100 Busy Traffic1x10 -5 70 Conversation3x10 -6 65 Whisper1x10 -10 20 Rustle of leaves1x10 -11 10 Hearing Threshold1x10 -12 1

31. Sound Level - Decibel

32. Ears judge loudness on a logarithmic vice linear scale Alexander Graham Bell deci = 1 bel = 10 decibel Why the decibel?

33. Reference Level Conventions Location Reference Intensity Reference Pressure Air1 x 10 -12 W/m 2 20  Pa Water6.67 x 10 -19 W/m 2 1 uPa

34. Historical Reference 1 microbar 1 bar = 1 x 10 5 Pa 1  bar = 1 x 10 5  Pa So to convert from intensity levels referenced to 1  bar to intensity levels referenced to 1  Pa, simply add 100 dB

35. Sound Pressure Level Mean Squared Quantities: Power, Energy, Intensity Root Mean Squared Quantities: Voltage, Current, Pressure “Intensity Level” “Sound Pressure Level”

36. Example Tube with a piston driver –a=2.5 cm –f = 1 kHz –154 dB in air What are the –rms piston displacement –intensity –power

37. Spherical Waves Standing wave n=0,1,2,3,… m=-n,…,+n Traveling wave

38. Spherical Waves For Us