Chapter 10, Problem 51R

To determine

The time taken by the sonar pulse to return.

Answer to Problem 51R

The required time is $\boxed{t=3.2\text{ s}}$ .

Explanation of Solution

Given:

The speed of sound in seawater, $v=\text{ 15}00\text{ m}/\text{s}$ and the distance is, $\lambda =\text{ 24}00\text{ m}$ .

Formula used:

The expression for time of a pulse to return is,

$t=2\lambda /v$   ..... (1)

Here, $\lambda$ is the wavelength of the note, v is the velocity of sound, $f$ is the frequency and $t$ is the time.

For a sonar pulse to return it has to travel twice the distance.

Calculation:

Substitute $\text{15}00\text{ m}/\text{s}$ for v and $\text{24}00\text{ m}$ for $\lambda$in equation (1),

$\begin{array}{l}t=\frac{2\times 2400}{1500}\\ t=3.2\text{ s}\end{array}$

Conclusion:

Hence, the required time is $3.2\text{s}$ .