Chapter 14.5, Problem 37E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

The speed of sound traveling through ocean water with salinity 35 parts per thousand has been modeled by the equation

where *C* is the speed of sound (in meters per second), *T* is the temperature (in degrees Celsius), and *D* is the depth below the ocean surface (in meters). A scuba diver began a leisurely dive into the ocean water; the diver’s depth and the surrounding water temperature over time are recorded in the following graphs. Estimate the rate of change (with respect to time) of the speed of sound through the ocean water experienced by the diver 20 minutes into the dive. What are the units?

To determine

**To estimate:**

The rate of change (with respect to time) of the speed through the ocean water experienced by the diver

Explanation

**1) Concept:**

Â By using chain rule, we find the rate of change of the speed through the ocean water

The Chain Rule:

Suppose that

**2) Given:**

**3) Calculation:**

As the speed of sound traveling through the ocean water with salinity

Differentiating

Similarly, Differentiating

Therefore, the rate of change of the speed of sound through the ocean water experienced by the diver into the dive is obtained by differentiating

Therefore, by applying chain rule,

From given graph,

At

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