A
circular diaphragm 60 cm in
diameter oscillates at a frequency of 25 kHz
in an underwater source of sound used for
submarine detection. Far
from the source the sound intensity is distributed as a diffraction
pattern for a circular hole whose diameter equals that of the
diaphragm. Assuming
that the speed of sound in water to be
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Solution: Click For PDF Version (a)
The speed of
sound in water is
The wavelength of sound waves of frequency 25 kHz will be
In a diffraction from a circular hole of diameter a the position of first minima is determined by the relation
It is given that the diameter of the circular diaphragm is
Therefore,
angle
(b) Let us repeat the calculation for oscillation of diaphragm with 1.0 kHz frequency. The wavelength of the sound waves will be
As
and cannot be
satisfied for any
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,
we have to find the angle between the normal
to the diaphragm and the direction of the first minimum.
(b) We have to repeat the calculation for a
source having an (audible)
frequency of 1.0 kHz.
.
.
will be
,
we may not be able to see the first diffraction minimum. Note
,