question_answer

A man fires a bullet standing between two cliffs. First echo is heard after 3 s and second echo is heard after 5 s. If the velocity of sound is 330 m/s, then the distance between cliffs is :

A)  660m                                   

B)  990m

C)  1320m                                 

D)  1950m

Correct Answer: C

Solution :

                 Echo is defined as the reflection of a sound wave back to its source in sufficient strength and with a sufficient time lag to be separately distinguished. \[\text{Time = }\frac{\text{distance}}{\text{speed}}\] Given that first echo is heard after 3 s, hence time taken for the echo to travel from first cliff to man is \[{{t}_{1}}=\frac{3}{2}=1.5\,s\] Similarly, time taken for the echo to travel from second cliff to man is \[{{t}_{2}}=\frac{5}{2}=2.5\,s\] Distance between man and first cliff is \[{{d}_{1}}=time\times velocity=1.5\times 330=495\text{ }m\] Distance between man and second cliff is \[{{d}_{2}}=time\times velocity=2.5\times 330=825\text{ }m\] Hence, distance between two cliffs is \[={{d}_{1}}+{{d}_{2}}=495+825=1320\,m\]