In the clinical use of ultrasound, transducers are always coupled to the skin by a thin layer of gel or oil, replacing the air that would otherwise exist between the transducer and the skin. 

(a) Using the values of acoustic impedance given in Table 17.5 calculate the intensity reflection coefficient between transducer material and air. 

(b) Calculate the intensity reflection coefficient between transducer material and gel (assuming for this problem that its acoustic impedance is identical to that of water). 

(c) Based on the results of your calculations, explain why the gel is used.

Data given in Table 17.5

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Air Water Blood Fat Medium Muscle (average) Bone (varies) Barium titanate (transducer material) 1.3 Density (kg/m³) 1000 1060 925 1075 1400-1900 5600 Speed of Ultrasound (m/s) 330 1500 1570 1450 1590 4080 5500 429 Acoustic Impedance (kg/(m².s)) 1.5 X 106 1.66 x 106 1.34 x 106 1.70 x 106 5.7 x 106 to 7.8 x 106 30.8 x 106