FUNDAMENTALS OF ACOUSTICS 18

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FUNDAMENTALS OF ACOUSTICS (18)

• RADIATION OF SOUND (2)

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The radiation of point sources

• Two point sources with same phase
• Consider two simple sources of equal strengths,
  separated by a distance d, vibrating with the
  same frequency and same phase.
• The pressure at a field point is the sum of the
  pressures produced by the individual sources.

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The pressure at point A due to source 1 is
and that due to source 2 is
Where r is the distance from the field point A to
the midpoint between the sources
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The acoustic pressure at (r , )is then

Attention to the far field
gtgt
Sound waves produced by tow point sources have
pronounced directional effects known as the
directivity of the source.
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The directivity of the source

• The directivity pattern of a sound source is a
  graphical description of the response of a
  radiator as a function of the direction of the
  transmitted waves

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The directivity function
Radiation of sound will be found equal to zero at
certain angles from the maximum of the axial
direction of the source, which is called the
directivity acute angle
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• Beam width is defined as the angle at which sound
  pressure drops down to a certain value( -6dB)
• The second maximum, called the side or minor
  lobe, is much weak than the first maximum
• We discuss the directivity function of two point
  sources.

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When
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1.When
In these direction, We have two sound waves of
same magnitude and phase , hence
2.When
In these direction, we have two sound waves of
equal magnitude but 1800 out of phase with each
other.
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• 3.When

ltlt
ltlt
We can obtain a polar plot of pressure( in dB)
versus angular displacements as shown in the
following Fig., which is the radiation pattern or
directivity of this particular arrangement of two
point sources.
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In general , the larger the extent of the
radiator (here we mean the spacing between the
sources), the sharper will be the major lobe and
the greater the number of side lobes.
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The simple line array

• Consider a line of N simple sources with adjacent
  elements spaced distance b apart, as shown in
  Fig.
• If all sources have the same source strength and
  radiate waves with the same phase, then the i th
  source generates a pressure wave of the form

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• resultant pressure at the field point is the
  summation

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• If we restrict attention to the far field(
  specified by the condition rgtgtd), we can
  approximate by assuming all ri are parallel.
• In far field ,ri in amplitude can be replaced
  with r

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Dipole radiation

• Homework
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