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Given the task of maximizing the transmission of sound waves from water into steel,
(a) what is the optimum characteristic impedance of the material to be placed between
the water and the steel? (b) What must be the density of, and sound speed in, a layer
of 1 cm thickness that will produce 100% transmission at 20 kHz?

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(a) To appreciate the human ear’s twelve order of magnitude (10^12) span from barely audible to the pain threshold, consider the following. Suppose an equivalently dynamic instrument were designed to measure distances. Taking the lower limit of the instrument to be 1.00 mm, what would be the largest distance measurable? (b) To provide a perspective for the human ear’s frequency sensitivity range (audible frequency extremes differ by 10^3 ), consider a speedometer with a similar speed range. If the speedometer’s maximum speed reading is 90.0 mi/h, what is the smallest finite speed that it could register?
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(a) To appreciate the human ear’s twelve order of magnitude (1012) span from barely audible to the pain threshold, consider the following. Suppose an equivalently dynamic instrument were designed to measure distances. Taking the lower limit of the instrument to be 1.00 mm, what would be the largest distance measurable? (b) To provide a perspective for the human ear’s frequency sensitivity range (audible frequency extremes differ by 103 ), consider a speedometer with a similar speed range. If the speedometer’s maximum speed reading is 90.0 mi/h, what is the smallest finite speed that it could register?
b) Given that the attenuation constant for TEM waves propagating on an air-filled cable is: α R 4πZ a b wp 20 +2) where R and Z₁ = 60 In In (1) Where a and b are the inner and outer radii of the cable respectively. Show that for minimum losses the ratio of the inner and outer radii is b/a = 3.6. Evaluate the corresponding characteristic impedance. HINT: Partially differentiate with respect to a holding b constant