Chapter 14, Problem 18E

The speed of sound traveling through ocean water is a function of temperature, salinity, and pressure. It has been modeled by the function

C = 1449.2 + 4.6T − 0.055T² + 0.00029T³ + (1.34 − 0.01T)(S − 35) + 0.016D

where C is the speed of sound (in meters per second), T is the temperature (in degrees Celsius), S is the salinity (the concentration of salts in parts per thousand, which means the number of grams of dissolved solids per 1000 g of water), and D is the depth below the ocean surface (in meters). Compute ∂C/∂T, ∂C/∂S, and ∂C/∂D when T = 10°C, S = 35 parts per thousand, and D = 100 m. Explain the physical significance of these partial derivatives.