91Ó°ÊÓ

Echo: The reflected sound heard by an observer after minimum 0.1 s of the original incident sound is known as echo.

The chirp is \(t = 3.0\,{\rm{ms}}\) long.

The difference between one to the next pulse is \(T = 70.0\;{\rm{ms}}\).

It is \(70.0\,{\rm{ms}}\) from the beginning of one chirp to the beginning of the next.

It is \(t' = \left( {70.0\,{\rm{ms}} - 3.0\,{\rm{ms}}} \right) = 67.0\,{\rm{ms}}\) from the end of one chirp to the beginning of the next. That means the time it takes for the pulse to travel from the bat to the moth and back is\(67.0\,{\rm{ms}}\). The sound should reach the moth and return during the\(67.0\,{\rm{ms}}\).

The distance to the moth is half the distance that the sound can travel\(67.0\,{\rm{ms}}\). The distance will be,

\(d = \frac{1}{2}vt'\)

Here,\(v = 343\;{\rm{m/s}}\)is the speed of sound in air.

Substitute the values and get,

\(\begin{array}{c}d = \left( {343\,{\rm{m/s}}} \right)\frac{1}{2}\left( {67.0\,{\rm{ms}}} \right)\\ = \left( {343\,{\rm{m/s}}} \right)\frac{1}{2}\left( {67.0 \times {{10}^{ - 3}}\,{\rm{s}}} \right)\\ \approx 11.5\;{\rm{m}}\end{array}\)

Hence, the moth should be detected\(11.5\;{\rm{m}}\)away.