$A$ man is standing between two parallel cliffs and fires a gun. If he hears the first and second echoes after $1.5 \, s$ and $3.5 \, s$ respectively,the distance between the cliffs is .... $m$ (Velocity of sound in air $= 340 \, ms^{-1}$)

  • A
    $1190$
  • B
    $850$
  • C
    $595$
  • D
    $510$

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Assume that the displacement $(s)$ of air is proportional to the pressure difference $(\Delta p)$ created by a sound wave. Displacement $(s)$ further depends on the speed of sound $(v)$,density of air $(\rho)$,and the frequency $(f)$. If $\Delta p \approx 10 \, Pa$,$v \approx 300 \, m/s$,$\rho \approx 1 \, kg/m^3$,and $f \approx 1000 \, Hz$,then $s$ will be of the order of (take multiplicative constant to be $1$).

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