Physics Assignment | Sound Physics

Added on - 28 May 2020

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SOUND PHYSICSQuestion 1It was recently discovered that gold bars (density 19.32 g/cm3) have been adulterated with acheaper metal ofsimilar density such as Tungsten (density 19.25 g/cm3). It has been proposedthat ultrasonic probes can be usedto detect the presence of a different metal in the gold. Formore information please visit the following websites: the relative sizes of the reflected longitudinal beams that would be received by anultrasonic probe i.e.the relative size of the beam reflected off the tungsten layer and the beamreflected off the back wall (20 marks)SOLUTIONSensitivity is the capability of an ultrasonic system to detect defects at a certain depth in a testmaterial. 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 theway ultrasonic waves traverse the metal. The pattern of wave reflections is changed by inserts ofmaterial which is not gold in a bar, a response that can also result due to internal voids. Hugeinserts that cover much of the volume of the bar can also be noticed by means of changes insound velocity.
i.Relative size of TungstenTungsten longitudinal velocity is calculated as shown;Where:VL=LongitudinalWave VelocityE=Modulus ofElasticity which is= 411=Density which is =19.25=Poisson's Ratiowhich is 0.284VL= 5.25 M/SZ= pcZ= acoustic impedanceC= material sound velocityP= material density
Z= 19.25×c= 19.25 ×c (longitudinal wave velocity)= 19.25 × 5.25 m/s=101.0625ii.Beam of backwallZ= pcZ= acoustic impedanceC= material sound velocityP= material densityZ= 19.32×c= 19.32 ×c (longitudinal wave velocity)= 19.32 × 3240 m/s=62,596.8Db loss (amplitude loss)= 10 log10(4 z1z2/(z1±z2)2)= 10 log10(4 ×101.0625×62596.8/(101.0625±62596.8)2)
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