## Related questions with answers

After determining the frequency of the waves in the previous problem, you then use a handheld sonar system to determine the ocean depth at $10.0-\mathrm{m}$ increments from the shore. The data are shown in the table. Complete the table and construct a graph of the wave speed as a function of the depth.

Distance $(\mathrm{m})$ | Depth $(\mathrm{m})$ | Speed $(\mathrm{m} / \mathrm{s})$ | Wavelength $(\mathrm{m})$ |
---|---|---|---|

$10.0$ | $1.4$ | ||

$20.0$ | $2.8$ | ||

$30.0$ | $4.2$ | ||

$40.0$ | $5.6$ |

Solution

Verified**Requirement**

In this task, we are required to determine the speeds and wavelength of different waves at differing depths, as well as plot the wave speed versus depth.

**Key concepts**

In fairly shallow (or acceptably shallow) water, the speed of the wave can be approximated using the relation:

$\begin{align} \mathrm{v\approx\sqrt{g \cdot d}} \end{align}$

where d is depth.

Speed and frequency are correlated to yield wavelength using the formula:

$\begin{align} \mathrm{\lambda=\frac{v}{f}} \end{align}$

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