Electro-Acoustical Engineering - Formula Sheet

Fundamental Wave Parameters

Parameter	Symbol	Relations	Units
Speed of Sound			m/s
Wavenumber			rad/m
Wavelength			m
Angular Freq.			rad/s
Frequency			Hz
Period			s

Wave Equations & Solutions

1-D Sinusoidal Waves

• Forward Propagating:
• Backward Propagating:
• General Wave Equation:

Waves on a String

• Wave Speed: (: tension, : linear density )
• Wave Equation:
• Fixed Ends (Length ):
  • Solution:
  • Modes: , , ()

Waves in Tubes

• Conservation of Mass:
• Newton’s Law (Euler):
• Resonant Frequencies ():
  • Open-Open / Closed-Closed:
  • Open-Closed:

Acoustic Impedance & Lumped Elements

• Acoustic Impedance:
• Specific Acoustic Impedance:
• Short Tubes ():
  • Acoustic Mass (Inductor):
  • Acoustic Compliance (Capacitor):
  • Acoustic Resistance (Resistor): (Long tube termination)

Helmholtz Resonator ()

• Front/Back Resonance: ,
• Helmholtz Resonance:

Power, Intensity & Decibels

• Acoustic Intensity (): (Plane wave)
• Acoustic Power ():
• Spherical Wave (Point Source):
  • Pressure:
  • Intensity:
  • Power:
  • Source Strength:

Decibels & Sonar Equation

• Sound Power Level (PWL):
• Sound Pressure Level (SPL):
• Source Level (SL):
• Transmission Loss (TL):
• Reference Values:
  • Reference power:
  • Reference distance:
  • Reference pressure (Air):
  • Reference pressure (Water):

2D/3D Waves & Spatial Modulation

• 2D/3D Plane Wave: ,
• Snell's Law:
• Normal Incidence Interface:
  • Reflection:
  • Transmission:
  • Energy: ,

Spatial Modulation ()

• Transfer Function:
• Wave Steering:
• Wave Focusing at :
• Wave Focusing at :
• Diffraction Grating:
• Sinusoidal Amplitude Grating: orders
• Sinusoidal Phase Grating: