Question

A person standing between two parallel hills fires a gun. He hears the first echo after 1.5 sec and second echo after 2.5 sec. If the speed of a sound is 332 $ms^{-1}$, the distance between the hills is

• A. 654 m
• B. 664 m
• C. 674 m
• D. 684 m

Hint:

Total distance = $\frac{v(t_{1} + t_{2})}{2}$. Just add the times and multiply by speed divided by 2.

Answer 1

The Correct Option is B

Step 1: Concept
An echo is heard when sound travels to a reflecting surface and back. The distance $d = \frac{v \times t}{2}$.

Step 2: Meaning
Let the distance from the person to hill 1 be $d_{1}$ and to hill 2 be $d_{2}$. Total distance $D = d_{1} + d_{2}$.

Step 3: Analysis
$d_{1} = \frac{332 \times 1.5}{2} = 166 \times 1.5 = 249$ m. $d_{2} = \frac{332 \times 2.5}{2} = 166 \times 2.5 = 415$ m.

Step 4: Conclusion
Total distance $D = 249 + 415 = 664$ m. Final Answer: (B)