Chapter 3.3, Problem 19E

Sound Speed in Oceans Marine scientists use a linear model for the speed c of sound in the oceans as a function of the salinity S at a fixed depth and temperature. In the following table, one scientist recorded data for c and S at a depth of 500 meters and a temperature of 15 degrees Celsius. Here c is measured in meters per second and S in part per thousand.

Salinity S	Sound speed c
$35.0$	$1515.36$
$35.6$	$1516.08$
$36.2$	$1516.80$
$36.8$	$1517.62$
$37.4$	$1518.24$

a. Looking over the table, the scientist realizes that one of the entries for sound speed is in error. Which entry is it, and what is the correct speed?

b. Explain in practical terms the meaning of the slope of the linear model for c in terms of S at the given depth and temperature.

c. Calculate $c\left(39\right)$ and explain in practical terms what it means.