Acoustic Variables • Pressure • Density – Condensation • Velocity (particle) • Temperature
Sound Speed Please Memorize!!!
Necessary Differential Equations to Obtain a Wave Equation • Mass Continuity • Equation of State • Force Equation – N2L Assumptions: homogeneous, isotropic, ideal fluid
Equations of State Ideal Gasses: Real Fluids:
Lagrangian and Eulerian Variables • Eulerian – Fixed Moorings • Lagrangian – Drifting Buoys Convective Term Material, substantial or Lagrangian Derivative Eulerian Derivative
Specific Acoustic Impedance Mechanical Impedance For a plane wave: In general:
Sound Speed Analogous to E-M wave impedance
Shorthand z Direction Cosines y x Propagation Vector Surfaces (planes) of constant phase
Average Power and Intensity A cdt For plane waves
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.
Why the decibel? • Ears judge loudness on a logarithmic vice linear scale • Alexander Graham Bell • deci = • 1 bel = 10 decibel
Historical Reference • 1 microbar • 1 bar = 1 x 105 Pa • 1 mbar = 1 x 105mPa • So to convert from intensity levels referenced to 1 mbar to intensity levels referenced to 1 mPa,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
Sound Pressure Level Mean Squared Quantities: Power, Energy, Intensity “Intensity Level” Root Mean Squared Quantities: Voltage, Current, Pressure “Sound Pressure Level”
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
Spherical Waves Standing wave n=0,1,2,3,… m=-n,…,+n Traveling wave