F300 Physics

Question 1

It was recently discovered that gold bars (density 19.32 g/cm3) have been adulterated with a cheaper metal of similar density such as Tungsten (density 19.25 g/cm3). It has been proposed that ultrasonic probes can be used to detect the presence of a different metal in the gold. For more information please visit the following websites:
http://www.olympus-ims.com/en/applications/ut-testing-gold-bars/
http://testyourgold.com/how-ultrasound-tests-gold-and-silver/

Estimate the relative sizes of the reflected longitudinal beams that would be received by an ultrasonic probe i.e. the relative size of the beam reflected off the tungsten layer and the beam reflected off the back wall (20 marks)

Solution

Sensitivity is the capability of an ultrasonic system to detect defects at a certain depth in a test material.  The transducer system is more sensitive when the received signal is greater.

 Adulteration of a gold bar by the method of inserts will result in predictable variations in the way ultrasonic waves traverse the metal. The pattern of wave reflections is changed by inserts of material which is not gold in a bar, a response that can also result due to internal voids. Huge inserts that cover much of the volume of the bar can also be noticed by means of changes in sound velocity.

Relative size of Tungsten

As ultrasound passes via a medium it attenuates. There are 3 causes of attenuation: diffraction, scattering and absorption, assuming no major reflections.

Assumptions

1. Sound velocity is dependent on the elasticity and density of the solid.
2. On a material denser than the external medium, reflected light undergoes a 180° phase reversal.
   
   

State any assumptions made. Please note that Tungsten has a Young's modulus is 411 GN/m2, and a poisson's ratio is 0.284 and Gold has longitudinal wave velocity of 3240 m/s.
A standard gold bar which has a standard thickness of 8.3 mm, has 6 mm of tungsten inserted in the middle. If we use an ultrasonic probe to measure the thickness using longitudinal waves, what thickness would be found?

Solution

Ultrasonic vibrations travel just the same as light in the form of a wave. The difference is ultrasound requires an elastic medium such as a solid or liquid while light can travel even in a vacuum. 

Shear modulus G= V_T²× density

⁼ 3240²(10^±8) ×19.32

=2.02

Young Modulus =

L,,=

convert the given values to units of time assuming you are using pulse-echo. So, the thickness of tungsten is calculated as follows

(8.3 × 2)÷3.24 = 5.123 time through Gold

(6 × 2) ÷ 3.24 = 3.7 time through both Gold and Tungsten

5.123- 3.7= 1.423 the difference in time

1.423 × 5.25 = 7.47mm the thickness of Tungsten

Assumptions

1. The longitudinal waves are identical with wavesin air.
2. It is possible to measure the thicknessof gold sheet within sub-micron accuracy

Using all the above information, find the values of a and b in the following line equation that relates the measured thickness, d, with the thickness of tungsten, dt: dt = a(b -d) (10 marks)

Measured thickness = d

Thickness of Tungsten dt: dt = a(b -d)

L,,= d =  

dt: dt = a(b -d)

L,,= d =  

a =  

b=  

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