Question

A man stands in a narrow, steep-sided valley. When he shouts he hears two echoes, one after 1 sand other after 2s. If the velocity of sound in air is 330 m/s, the width of the valley is

• A. 330m
• B. 495m
• C. 660m
• D. 990m

Answer 1

Answer: (B)

Let $ {{s}_{1}} $ and $ {{s}_{2}} $ be the distances of man from either side of valley, then $ 2{{s}_{1}}=v{{t}_{1}} $ and $ 2{{s}_{2}}=v{{t}_{2}} $ $ \Rightarrow $ $ 2({{s}_{1}}+{{s}_{2}})=v({{t}_{1}}+{{t}_{2}}) $ $ \Rightarrow $ $ {{s}_{1}}+{{s}_{2}}=\frac{v({{t}_{1}}+{{t}_{2}})}{2} $ $ \therefore $ $ d={{s}_{1}}+{{s}_{2}}=\frac{330\times (1+2)}{2} $ $ \Rightarrow $ $ d=\frac{330\times 3}{2}=495\,m $