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Sound Waves in Physics

Sound is a pressure wave, so what the ear hears is really a squeezed and stretched column of air rather than anything moving towards you. The particles only vibrate about their own places, and the loudness you perceive is the energy those vibrations carry per second, which is why the ear responds to sound on a logarithmic scale. What makes sound especially useful is that its speed is fixed by the air rather than by the source, so a moving source or a moving listener can shift the pitch without changing the note being played. The blocks give the pressure and displacement relation, the speed in each kind of medium, the intensity and its decibel scale, and the Doppler shifts that follow from relative motion.

Pressure amplitude from the displacement amplitude

Given

  • (kg/m³)
  • (m/s)
  • (rad/s)
  • (m)
Pressure variation at a point in a sound wave

Given

  • (Pa)
  • (rad/m)
  • (rad/s)
  • (m and s)
Displacement of the particles in a sound wave

Given

  • (m)
  • (rad/m)
  • (rad/s)
  • (m and s)
Speed of sound in air from the temperature

Given

  • (°C)
Speed of sound in a medium from its bulk modulus

Given

  • (Pa)
  • (kg/m³)
Speed of sound in an ideal gas

Given

  • (K)
  • (kg/mol)

Constant used

Wavelength of a sound wave

Given

  • (m/s)
  • (Hz)
Intensity of a periodic sound wave

Given

  • (kg/m³)
  • (m/s)
  • (rad/s)
  • (m)
Intensity of sound spreading from a point source

Given

  • (W)
  • (m)
Sound intensity level in decibels

Given

  • (W/m²)
  • (W/m²)

Constant used

Intensity from a sound intensity level

Given

  • (dB)
  • (W/m²)

Constant used

Doppler effect with both source and observer moving

Given

  • (Hz)
  • (m/s)
  • (m/s)
  • (m/s)
Doppler effect for an observer moving towards a stationary source

Given

  • (Hz)
  • (m/s)
  • (m/s)
Doppler effect for a stationary observer with the source approaching

Given

  • (Hz)
  • (m/s)
  • (m/s)
Doppler shift of a source moving away from a stationary observer

Given

  • (Hz)
  • (m/s)
  • (m/s)
Mach number of a source moving through air

Given

  • (m/s)
  • (m/s)
Half angle of the shock cone behind a supersonic source

Given

  • (m/s)
  • (m/s)