Four Chapter 10

• Stationary sources radiate sound in concentric circles around the source.
  • Moving sources radiate sound in spheres around successive positions.

• At the speed of sound, all the compressions pile up in one spot to produce very dense air.

• Sound Barrier – The compression of very dense air that forms when objects move at the speed of sound.
  • Improperly designed air craft would be buffeted about by this compression.
  • If properly designed, the aircraft will cut through this barrier without problem and leave the sound behind.
• When travelling faster than sound, the spheres interfere to produce large compressions and rarefactions, which sweep behind the aircraft in a cone shape.
• This cone sweeps across the ground to produce a sonic boom (2 sharp cracks, one for each side of the cone as it passes over).
• The cone is usually five times as wide as the aircraft is high.
• Sonic booms usually do not cause damage but they could affect ecosystems if it occurs frequently.

• When a car speeds by you notice that the pitch of the horn decreases as it passes.
• Wave fronts in front of the car are close together and behind are far apart.

• C hears a higher than normal pitch.
• A hears a lower than normal pitch.
• B hears a pitch that changes from high to low.
• The driver hears the normal pitch.
• Doppler effect – The apparent change in frequency of a wave due to relative motion between source and observer.
  • If the relative motion is towards, the pitch increases.
  • If the relative motion is away, the pitch decreases.
• The equation used to determine the apparent observed frequency is

• f₁ = true frequency of the wave
• f₂ = apparent frequency of the wave
• v = Speed of sound
• v_o = Speed of the observer
• v_s = speed of the source
• The rule of signs

• The Doppler effect occurs for any object emitting waves. The equation for the Doppler effect is different for light because light does not have a medium that it moves through. For light we have
  • For source and observer approaching each other

• For source and observer separating from each other

• f’ = observed frequency.
• f = actual frequency.
• v = relative velocity between observer and source.
• Applications of the Doppler effect include determining the speed of cars by the police, and the speed of stars with respect to the Earth.

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November 18, 2013