FUNDAMENTALS OF ACOUSTICS 16

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FUNDAMENTALS OF ACOUSTICS (16)

• Sound waves travel in the pipe

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Each
has its own characteristic eigenfrequency
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The limiting value of for which kz remains
real ,This defines the cutoff frequency
Characteristic eigenfrequency
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3. The nx, ny mode

• 1. (0,0) order mode
• 2. (nx ny) order mode

For (0,0) order, the pressure is
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• Depend on if it can be stimulated by the source
  frequency
• Example
• A rectangular cavity , with source frequency is
  100Hz

From
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The lowest characteristic eigenfrequency is
In this case , there is only ordinary plane
waves travel in the pipe
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If for (0,1)

• Cutoff frequency ------????
• The lowest characteristic eigenfrequency other
  than (0,0)

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Geometry figure of high order waves
(1,0)
(2,0)
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Physical expression

• High order wave consists of several group of
  planes. And these planes are traveled at angle

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Which means there are not high order waves travel
in the z direction (except
Is cutoff frequency
(nx,0 ) high order waves can not travel in z
direction
(nx,o) high order waves can travel in z direction
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Example

• Consider high order waves (nx1, ny0)
• Can it travel in the rectangular cavity with

is large in any size ?
For
so
can travel in the rectangular cavity
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Corresponding high order waves can travel in z
direction

• Corresponding high order waves can not travel in
  z direction, these waves decay in z direction
• Consider the high waves attenuation

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• A rectangular cavity with cross section area is
  0.150.15m2,we can calculate it cutoff frequency
  is1130Hz?If at z0 source frequency is
  f565Hz,then
• At z0.1m,got
• For the vibrations of(0,1)and(1,0),The amplitude
  at z0.1m will be great attenuation ?For the
  higher than (0,1)and(1,0) order waves ,the
  amplitude will decay more rapidly ,thus ,at
  curtained distance ,there is only a corresponding
  a major wave

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• If source frequency is close to cutoff frequency
  ,such as f1130Hz,we can get

• The sound pressure in the pipe will be

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• It express that there is a major wave(0,0)and
  superimpose the high order waves(0,1)and
  (1,0)which do not decay
• This is the standing waves vibration in x,y
  direction?In this case the sound field is become
  more complex.

• (4)the speed of high order waves traveling in the
  pipe (see text book)?

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3-11-3 sound waves travel in the cylindrical
cavity

• From the wave equation

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B0
z0, zl
ra
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is the solutions of
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In z direction
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Homework

• Text book P277
• 3-19
• 3-20