Ch. 15 - Wave Motion

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 15 - Wave Motion

Problem 8

Chapter 15, Problem 8

A sailor strikes the side of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 2.4 s later. How deep is the ocean at this point? (Use Tables 12–1 and 13–1.)

Verified step by step guidance

Determine the total time taken for the sound wave to travel to the ocean floor and back. The problem states that the sailor hears the echo 2.4 seconds later, so this is the round-trip time.

Recognize that the time for the sound to travel one way (to the ocean floor) is half of the total time. Therefore, divide the total time by 2 to find the one-way travel time.

Use the formula for distance:

d = v \cdot t

, where

d

is the depth of the ocean,

v

is the speed of sound in seawater, and

t

is the one-way travel time.

From the problem, refer to the provided tables (Tables 12–1 and 13–1) to find the speed of sound in seawater. Typically, the speed of sound in seawater is approximately 1500 m/s, but confirm this value from the tables.

Substitute the values for

v

(speed of sound) and

t

(one-way travel time) into the formula to calculate the depth of the ocean. Ensure the units are consistent throughout the calculation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Speed of Sound in Water

The speed of sound in water is approximately 1482 meters per second at room temperature. This speed is crucial for calculating the distance sound travels in water, as it determines how quickly the echo from the ocean floor returns to the sailor. Understanding this speed allows us to relate the time taken for the echo to the depth of the ocean.

Echo and Time Delay

An echo is a reflection of sound that arrives at the listener after a delay. In this scenario, the sailor hears the echo 2.4 seconds after striking the ship's side. This total time includes both the time for the sound to travel down to the ocean floor and back up, which is essential for calculating the depth of the ocean.

Distance Calculation

To find the depth of the ocean, we use the formula: distance = speed × time. Since the time measured is for the sound to travel to the ocean floor and back, we must divide the total time by two to find the one-way travel time. This allows us to accurately calculate the depth based on the speed of sound in water.

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