FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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As the scattering theory requires spherical defects, this work examines the scattering of a focussed
sound beam from spherical and near spherical bubbles in glass. The use of glass rather than opaque
ceramics facilitates optical characterization, the only way a small defect can ever be diagnosed.
II. THEORY
The pressure profile for the sound beam from a focussed transducer operating at a single frequency is
a complicated function of the density p and speed Î sound cL of the medium, the diameter D and
radius of curvature A of the transducer, and the frequency f. At the focal distance Zf from the
transducer the pressure is:
where
i2nflt - (ß + z.)]
2c, '
c, S fe
L zf
8nS
S = »
V 1 - A/Zf
(Zf - h)" + (D/2)"
sin {nf (p 1 - Zf )}
1/2
, h = A - A" - (D/2)-
and So is the displacement of the front face of the transducer. N'ear the focus the pressure function
can be approximated in the form of a plane wave as:
i2nf(t - AZ/Cjj
where AZ is the distance along the z-axis from the focal point. L'sing the theory of Ying and Truell
(4), the relative pressure amplitude for the longitudinal wave backscattered to the transducer from a
spherical void of radius, a, is:
p (f,a) -2n-e
f L
(2m
m = 0
where the scattering coefficients Am are determined from the stress and strain relationships at the
surface of the void. Now if the sound pressure at the site of the void were known it would be possible
to determine the pressure of a backscattered monochromatic longitudinal wave.
Reflections from the sample surfaces make single frequency studies impractical, fnstead, short
pulses of ultrasound are generated by shock excitation of the transducer so that the defect can be
located. A pulse of ultrasound is composed of many waves of different frequencies The distribution of
wave amplitudes and phases as a function of frequency is called the response function of the
transmitter-receiver system, R(f). Since the sound pressure is maximum at the focus the waves will
be in phase so that only the amplitude component of the response function needs to be considered
Experimentally the function is determined by routing to a spectrum analyzer the signal reflected
from a flat surface in the focal plane of the transducer. For the calculations the system response
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