Chapter 13, Problem 1GST

To determine

The time required for the echo sounder’s ping to make the trip from a ship to the Challenger Deep and back.

Answer to Problem 1GST

The time required for the echo sounder’s ping to make the trip from a ship to the Challenger Deep and back is calculated as $14.6\text{seconds}\text{.}$

Explanation of Solution

Given info:

$\text{Depth}\text{of}\text{Challenger}\text{Deep}=10994\text{meters}$

The equation for calculating water depth from echo sounding is given below:

$\text{Depth}=\frac{1}{2}(1500\text{m/sec×echo}\text{travel}\text{time})$

$1500\text{meters/second}(4900\text{feet})$ is the average speed of sound waves in water.

To calculate the time, rearrange the following equation:

$\text{Echo}\text{travel}\text{time}=\frac{\left(\text{depth}\times 2\right)}{\left(1500m/\sec \right)}$

Substitute the depth in the equation.

$\begin{array}{l}\text{Echo}\text{travel}\text{time}=\frac{\left(10994m\times 2\right)}{\left(1500m/\sec \right)}\\ =14.6\text{seconds}\end{array}$

Conclusion:

Thus, the time required for the echo sounder’s ping to make the trip from a ship to the Challenger Deep and back is $14.6\text{seconds}\text{.}$