A person is standing between two cliffs, suppose it takes at least t sec for an average human ear to differentiate between two sound waves. The person produces sound waves having velocity v, he is standing at distance `d_(1)` and `d_2` from the two cliffs. What is the relation between `d_(1), d_2`, v required so that he can distinctly hear both the echoes. What is the minimum value of `d_(1)` and `d_2` for the condition to happen?

Explanation

Let us say `d_(1) gt d_2`. So that he can hear both the echoes `(2d_(1))/(v) ge (2d_2)/(v)+t`
`implies (2d_2)/(v)ge t implies d_2 ge (vt)/(2)`
and `(2d_(1))/(v) ge 2t implies d_(1) ge vt`
Minimum `(d_(1) +d_2)` = minimum `(d_(1))` + minimum `(d_2)` = `(3vt)/(2)`