Chapter 11, Problem 43P

To determine

To Find: The depth at which echo of the wave is reflected.

Answer to Problem 43P

The depth of the ocean at which echo of the wave reflected from the ocean is $2.1\times {10}^3\text{m}$ .

Explanation of Solution

Given info:

Bulk Modulus of water, $B=2\times {10}^9{\text{ N/m}}^{\text{2}}$ ,

Density of water, $\rho =1000{\text{ kg/m}}^{\text{3}}$ ,

Distance, $d=2\times L$ ,

Time take to return, $t=3\text{ s}$ .

Formula used:

The expression for the speed of water wave $v$ ,

  $v\text{ = }\sqrt{\frac{\text{Bulk modulus of water}}{\text{Density of water}}}=\sqrt{\frac{\text{B}}{\rho }}$ .......equation (1)

Speed is also expression as:

  $v=\frac{\text{distance}}{\text{time}}=\frac{2\times L}{t}$   ...equation (2)

Here, $L$ is distance for echo.

Calculation:

Substitute the given values of bulk modulus and Density in the equation (1) to get the value of velocity,

  $v=\sqrt{\frac{2\times {10}^9}{1000}}=1414.21\text{ m/s}$

Substitute the value of $v$ in the equation (2) to get the value of $L$ .

  $\begin{array}{l}v\text{ = }\frac{\text{distance}}{\text{time}}\text{= }\frac{2\times L}{t}\\ L=\frac{v\times t}{2}=\frac{3\times 1414.21}{2}=2.1\times {10}^3\text{ m}\end{array}$

Conclusion:

Thus, the depth of the ocean at which echo of the wave reflected from the ocean is $2.1\times {10}^3\text{m}$ .