UNIVERSITY OF TORONTO

FACULTY OF APPLIED SCIENCE AND ENGINEERING

FINAL EXAMINATION, Friday April 19, 2017

9:30 - 12:00 am

DURATION: 2 and 1/2 hrs

Fourth Year - Mechanical and Industrial Engineering

M1E433H15 - Waves and their applications in Non-Destructive Testing and Imaging

Calculator Type: Any type

Exam Type: D

Examiner: Andreas Mandelis,

INSTRUCTIONS:

This is a two and one-half (2 ½) hour open-book exam. It is a type D test: Only the approved chapters from the course textbooks (see course outline), a single aid sheet (students may enter on both sides of the aid sheet any information they desire) and a calculator (any type, programmable or non-programmable) will be allowed during the final exam as the only aids to the student.

Attempt to solve all problems.

All problems carry equal weight.

Show all steps involved in solving each problem.

Give numerical answers to three significant digits with appropriate units.

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Problem 1:

An ultrasonic NDT system uses an acoustic filter to attenuate the noise level of surrounding equipment, so as to be able to perform measurements within an acoustic enclosure. If the filter decreases the sound level by 20 dB, what is the ratio of the final intensity If of the ultrasonic noise waves to the initial intensity I?

The sound intensity from a jackhammer breaking concrete is 2.0 W/m2 at a distance of 2.0 m from the point of impact. This is sufficiently loud to cause permanent hearing damage if the operator does not wear ear protection. What is the sound intensity for a person watching from 50 m away? What is the power generated by the sound source?

Problem 2:

Consider a simple example of two ultrasonic waves with slightly different velocities and frequencies: The longitudinal displacements of the transmission medium (e.g. water) are u1 (x,t) = Acos(k1 x—col t)

and u2 (XI t) = Acos(k2 x—w21)

with phase velocities of v1 = k j/w j and v2 = k2/w2. Here A is the (common) amplitude of the two waves. The total displacement is then:

Utoiai (x, I) = u1 (x, t) + u2 (x, t)

Write an expression for Utotai(X,t) in a form similar to the constitutive equations above,

in terms of k1, k2, w1, w2.

If to = to2 +Aw and k1 = k2 +Ak, where Ato << w1 ,w2 and Ak <<k1 ,k2 , use the

expression you found in (a) to find the group velocity of this wave

Problem 3:

The decay rate R of a radioactive nucleus is given by R(t) = - dN(t)

where N is the di

number of radioactive nuclei in a sample, given by N(t) = N0e', in which 2 is the

disintegration (or decay) constant for this radioactive element. No is the number of radioactive nuclei in the sample at some initial time t = 0. R is also called the "activity" of the sample and its SI unit is the bequerel (1 Bq = I decay per second). a) There are two common time measures of how long the radionuclide lasts. One is the half-life T]/2 which is the time at which both N and R have been reduced to one-half their initial values. The other measure is the mean life t, which is the time at which both N and R have been reduced to e1 of their initial values. Find a relationship between 1) T1/2 and

-r ; 2) T112 and 2c.

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b) The table below shows some measurements of the decay rate of a sample of 1281, a

radionuclide element often used in non-invasive medicine as a tracer to measure the rate at which iodine is absorbed by the thyroid gland.

Time (mm) R (counts/s) 4 392.2

36 161.4 68 65.5

100 26.8 132 10.9 164 4.56 196 1.86 218 1.00

From these data find the disintegration constant ?. and the half-life T1/2 for this radionuclide.

Problem 4:

In an X-ray generation instrument for non-destructive imaging applications X rays of wavelength 2 = 110 pm are scattered from a carbon target and emerge out of the target with wavelength shifted by 3.2 pm.

What percentage of the initial X-ray photon energy is transferred to an electron (Compton effect) in this scattering?

Assuming energy is conserved following the collision between the original X-ray and the electron, calculate the speed of the emerging electron after the collision.

Problem 5:

Infrared thermography measurements were performed on a test sample consisting of small plates of different materials bonded onto a 1-mm thick layer of fiberglass epoxy composite. Surface laser illumination was incident from the uniformly thick top (epoxy) layer, while the small plates were located below the upper layer. The figure below shows the normalized temperature image after a very short heating pulse. Normalization means that the surface temperature response T (0, t) of a semi-infinite overlayer thickness was

subtracted from that of the composite structure. The range of behaviors is shown more clearly in Figure (b) where the normalized temperature T(0, t) - T (0, t) is plotted as a

function of square root of time for pixel locations on each of the different materials. Why is a plot vs. square root of time appropriate for this type of thermographic signal

time evolution? Write an expression for T(0, t) - (0, t) to justify your answer

What can you conclude about the relative thermal properties of the various plate materials with respect to each other and the epoxy composite?

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E -

0 z gel

1.2 1,4 0 0.2 0.4 0.6 0.8 Square Root Time

[1/2]

(b)

* Aluminum :4 • A Fiber Glass

;ti_________ -as

a

-

-

[oj

C) By fitting an appropriate expression to the data in Fig. (b) what material parameters or groups of parameters can one estimate?

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