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UT Math Formulas
math formulas for L and S waves UT intro and intermediate San Jac
26
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Undergraduate 2
02/19/2015

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Term
thickness

T
Definition
given, usually
wavelength/2
Term
diameter

D
Definition
given, printed on transducer
one of the 2 variables you can control
Term
frequency

F
Definition
given, printed on transducer
one of the 2 variables you can control
Term
velocity

V
Definition
F*wavelength

or distance/time
Term

θ formula

 

theta

Definition

Sin^-1((1.22*λ)/(D))


answer in degrees

Term
Nearfield N
Definition
((D^2)/(4*λ))
Term
Remaining Distance

R
Definition
T-N
Term
X value
Definition
R*Tan(λ)
Term
Beam Spot size B.S.S.
Definition

2(X)+D

 

2*(X-value)+diamater 

Term
basic calculations
for drawing beam
Definition
T
D
F
V
wavelength
theta
N
R
X
B.S.S.
Term
snells law
Definition
sin^-1((V2/V1)Sin(θI))=R Sin^-1((V1/V2)Sin(θR))=I
Term
when Frequency (F) goes up

from relational chart
Definition
Wavelength- goes down
theta- down
Resolution (R)- up
Sensitivity (S)- up
Nearfield (N)- up
Penetration (P)- down
Term
when Diameter (D) goes up

from relational chart
Definition
Wavelength- = stays the same
theta- down
Resolution (R)- down
Sensitivity (S)- down
Nearfield (N)- up
Penetration (P)- up
Term
when Velocity (V) goes up

from relational chart
Definition
Wavelength- up
theta- down
Resolution (R)- down
Sensitivity (S)- down
Nearfield (N)- down
Penetration (P)- up
Term
Metal Path (MP) formula
Definition

(2*T)/cos(θ)=VeePath(middle#)


VeePath/2=1stLeg(1st#)


1stLeg*3=3rdLeg(3rd#)

Term
skip distance (SD) formual
Definition

(2*T)TAN(θ)=VeePath(middle#)


VeePath/2=1stLeg(1st#)


1stLeg*3=3rdLeg(3rd#)

Term
AATT absolute arrival time technique
Definition
T-(SP of tip peaked)*Cos(θR))=
Term
RATT relative arrival time technique
Definition
T-((MP of base-MP of tip)/(cos(θR))=
Term
what snells law does
Definition

calculates either the incident angle (sine of angle 1)


or the refracted angle (sine of angle 2)


for given velocities V1 and V2

Term
Sin theta 1=
Sin theta 2=
Definition
V1
V2
Term
angle of incidence (Sin θ1) formula
Definition
(Sin(θ2)*V1)/V2
Term
angle of refraction (Sinθ) formula
Definition
(Sin(θ1)*V2)/V1
Term
what acoustic impedance formula does
Definition
calculates the acoustic impedance (Z) of a given material's Density (P) and velocity(V)
Term
acoustic impedance formula and variations
Definition

Z=P*V

 

P=Z/V


V=Z/P


R=((Z2-Z1)/(Z2+Z1))^2


*P=density*

Term
X-value, what it is
Definition
 x-value of the probe, this is the distance of the sound exit point to the front edge of the probe
Term
wavelength=
Definition
V/F
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