Chapter 15, Problem 43A

To determine

To calculate: Distance between the man and the cliff.

Answer to Problem 43A

Distance between the man and the cliff = $\underset{\_}{340\text{ m}}$ .

Explanation of Solution

Given:

Temperature = $15°\text{C}$

Time taken for the echo to return = $2.0\text{ s}$

Formula used:

Distance for an echo is given by,

$d=\frac{1}{2}vt$

Where $v$ is velocity and $t$ is time taken.

Calculation:

Speed of sound in air at $0°\text{C}$ = $331\text{ m/s}$ . Speed of sound increases by $0.6\text{ m/s}$ for every $1°\text{C}$ rise in temperature. For $15°\text{C}$ rise in temperature, speed of sound will increase by $0.6\times 15=9\text{ m/s}$ .

Therefore, speed of sound at $15°\text{C}$ is $331+9=340\text{ m/s}$

Distance between man and cliff is calculated as:

$\begin{array}{l}d=\frac{1}{2}vt\\ \text{ =}\frac{340\text{ m/s}\times 2\text{ s}}{2}\\ \text{ =}340\text{ m}\end{array}$

Conclusion:

Distance between the man and the cliff = $\underset{\_}{340\text{ m}}$ .