WARNING! The formulae in this page are a TOTAL mess.

Sound Waves in Pipes

• Sound travels in pipes at the same speed that it travels in open air. It is not significantly affected by the cross-section shape of the pipe nor by bends or corners in the pipe.
• At a closed pipe end the sound must bounce, be reflected, from the closed end.
• At an open end the sound is also reflected. In order for the sound to diffract out of the open end of the tube a reflection must be generated travelling back up the tube.

Waves an Trays and in Pipes

Waves on a Tray At open end Slope is 0 Position varies most Wave reflected in phase At closed end Movement is 0 Slope varies most Wave suffers 180° phase change

Waves in a Pipe At open end Pressure is atmospheric so change in pressure is 0 Air can move freely, velocity is maximum. Wave reflected in phase. At closed end Air cannot move because wall is in way. Pressure can change freely, varies maximally. Reflected waves suffers 180° phase change.

Standing Waves

• Standing wave occurs when the phase of the wave after 1 round trip is the same as the phase of the initial wave.
• Change in phase = 360° Trip Time + diff. at reflect.
  Period
• Trip Time = Dist. Traveled = 2L , 1 = f
  Velocity v Period
• For standing wave
  Change in phase = 360° 2fL + diff. = 360° n
  v
  where n is an integer.

Tube open at both ends

• Reflections take place without phase shift.
• Total phase shift in 1 trip round tube
• Phase shift = 360° 2fL = 360° n
  v
• For standing wave f = n v or l = v = 2L
  2L f n
• Thus, in standing wave an integral number of half wavelengths fit in the tube,
  L = n l
  2
• The frequencies form a complete harmonic series.

Tube closed at one end

• Reflection takes place without phase shift, other adds 180° phase shift.
• Total phase shift in 1 trip round tube
• Phase shift = 360° 2fL + 180° = 360° n
  v
• For standing wave f = (2n-1) v or l = v = 4L
  4L f 2n-1
• Thus, in standing wave an odd integral number of quarter wavelengths fit in the tube,
  L = (2n-1) l
  4
• The frequencies form an incomplete harmonic series. The fundamental is 1 octave below that for an open tube of the same length and all even harmonics are missing.