Question

A stone is dropped from cliff into a lake 80 m deep. Another cliff which is 200 m away from the lake
reflects the sound of splash . What is the time difference between the sounds of the first splash
and echo of splash? Take speed of sound is 340 ms1 and g = 10 ms2

Answer 1

For 1st splash:

• The time taken for stone to reach water = √(2h/g).

• The time taken for reflected sound to reach observer = h/(340)

For echo:

• The time taken to for sound of splash to the 2nd cliff = √(2h/g) + 200/340 sec.

• Again that sound will be reflected back, time needed = 200/340 sec.

So, time difference will be :

$T = ( \sqrt{ \dfrac{2h}{g} } + \dfrac{200}{340} + \dfrac{200}{340} ) - ( \sqrt{ \dfrac{2h}{g} } + \dfrac{h}{340} )$

$\implies T = \dfrac{400}{340} - \dfrac{h}{340}$

$\implies T = \dfrac{400}{340} - \dfrac{80}{340}$

$\implies T = \dfrac{400 - 80}{340}$

$\implies T = \dfrac{320}{340}$

$\implies T = 0.94 \: sec$

So, time difference will be 0.94 sec.