FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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now _n = Af (5)
n
where Af is the spacing between consecutive frequency maxima which is the
slope of the plot of f vs n.
Plotting 2hfa—ß" vs tan ß wil1 y ield a strai Sht line with
gradient = d COSY (6)
and intercept = d sinY (7)
Thus, the diameter and orientation of the circular scatterer can be found
from
d = \ (gradient 2 + intercept 2 ) (8)
-1 /intercept \
' I gradient /
For d«D, it can be shown from simple trigonometry that
VAt = 2dsine (10)
where At is the difference in round trip travel time between the two opposite
edges of the circular scatterer.
Substituting Eq. (3) into Eq. (10) and rearranging terms
VAt
2 cos
= d cos y tan s + d sin Y
Plotting „ —— vs tan B will yield a straight line with gradient
c. COS p
and intercept again given by Eq. (6) and (7). Thus d and y can be found
from Eq. (8) and Eq. (9).
The methods described above thus show that ultrasonic frequency analysis and
time-of-flight method can independently yield information about d and Y of
a circular scatterer.
Using Eq. (2), (5) and (10), it can be shown that
AtAf ~ 1 (12)