Question

A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after $1$ second and the second echo after $3$ second. The distance between the two cliffs is (Velocity of sound $= 340\text{ m/s}$ )

• A. $340\text{ m}$
• B. $680\text{ m}$
• C. $1020\text{ m}$
• D. $1360\text{ m}$

Hint:

Echo formula: \[ d=\frac{vt}{2} \] because sound travels to the cliff and comes back.

Answer 1

The Correct Option is B

Concept:
Echo time is the round-trip time of sound: \[ t=\frac{2d}{v} \] ip

Step 1: Find distance to first cliff.
For first echo: \[ 1=\frac{2d_1}{340} \] \[ d_1=\frac{340}{2}=170\text{ m} \] ip

Step 2: Find distance to second cliff.
For second echo: \[ 3=\frac{2d_2}{340} \] \[ d_2=\frac{3\times 340}{2}=510\text{ m} \] ip

Step 3: Find distance between cliffs.
\[ d_1+d_2=170+510=680\text{ m} \] ip Hence, the correct answer is:
\[ \boxed{(B)\ 680\text{ m}} \]