Acoustic Wave Equation

# Acoustic Wave Equation

Télécharger la présentation

## Acoustic Wave Equation

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

1. Acoustic Wave Equation

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

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 Convective Term Material, substantial or Lagrangian Derivative Eulerian Derivative

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 Analogous to E-M wave impedance

22. Plane wave in an arbitrary direction

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

24. k in x-y plane

25. Energy

26. Energy Density

27. Average Power and Intensity A cdt For plane waves

28. Effective Average - RMS

29. 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.

30. Sound Level - Decibel

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

32. Reference Level Conventions

33. Historical Reference • 1 microbar • 1 bar = 1 x 105 Pa • 1 mbar = 1 x 105mPa • So to convert from intensity levels referenced to 1 mbar to intensity levels referenced to 1 mPa, simply add 100 dB

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

35. 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

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

37. Spherical Waves For Us