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Sound

• Sound waves are transmitted as a series of longitudinal pressure differentials.
• Depending on the medium and its specific conditions, the speed of sound can vary greatly.
• "High" pitches correlate to high frequency sound waves, "low" pitches correlate to low frequency sound waves.
• The intensity ("loudness") of a sound is determined by the power (P) of the source and the area (A) it is spread over:
  

  I = P A .

• If the source of the sound spreads perfectly evenly in all direction (which turns out to be difficult in the real world), we can model it with a sphere. The surface area of a sphere is A=4πr², which we can use with the above equation.
• The human ear can hear a huge variety of intensities. We manage this issue by introducing a logarithmic scale for measuring intensity: the decibel (dB).
• If you feel uncomfortable with logarithms, you might want to do a quick review of how they work. Check out the pre-calculus math section on Educator.com to get refreshed with logs.
• We define the idea of sound level (β) using decibels:
  

  β = (10 dB) ·log10 I I0 .

• Since waves can interfere with one another, if they have different frequencies, the waves will come in an out of phase with each other. This is the beat frequency:
  

  fbeat = |f1 − f2|.

• For objects traveling faster than the speed of sound, we can describe its speed with a Mach number: [v/(v_s)]. Mach 1 is the speed of sound, Mach 2 is twice the speed of sound, etc.