Chapter 12, Problem 87GP

To determine

To Find:The distance the bat and the moth.

Answer to Problem 87GP

The distance the bat and the mothis $11.5\text{m}$ .

Explanation of Solution

Given:

The time period of pulse, $\mathrm{T}=70\text{ms}$

The time taken by pulse, $\mathrm{t}=3\text{ms}$

The speed of sound in the air, $\mathrm{V}=343\text{m/s}$

Formula used:

The distance between the bat and the moth is calculated as:

  $\begin{array}{l}2\mathrm{d}=\mathrm{V}\times {\mathrm{T}}_{\text{signal}}\\ {\mathrm{T}}_{\text{signal}}=\mathrm{T}-\mathrm{t}\end{array}$

Here, $\mathrm{V}$ is the speed of sound in the air,

  $\mathrm{t}$ is the time taken by pulse.

Calculation:

Substitute the given values:

  $\begin{array}{l}{\mathrm{T}}_{\text{signal}}=70-3=67\text{ms}=0.067\text{s}\\ 2\mathrm{d}=343\times 0.067=22.981\\ \mathrm{d}=\frac{22.981}{2}=11.49=11.5\text{m}\end{array}$

Conclusion:

The distance between the bat and the moth is $11.5\text{m}$ .