Question

A man who is standing at a point X between two parallel walls as shown in the diagram, fires a starting pistol.
He hears the first echo after 0.6 s and another one after 0.8s.
How long after firing the pistol will he hear the next echo ?

• A. 1.2 s
• B. 1.4 s
• C. 1.6 s
• D. 2.4 s

Answer 1

The correct option is B 1.4 s

Let the first echo comes when sound reflected by $d_1$ distance.

$d_1=v_s\ast t_1\frac{1}{2}$

$d_1=v_s\ast 0.6\frac{1}{2}=0.3v_s$

Let the second echo comes when sound reflected by $d_2$ distance.

$d_2=v_s\ast t_2\frac{1}{2}$

$d_2=v_s\ast 0.8\frac{1}{2}=0.4v_s$

So, the third echo comes when sound traveled $2(d_1+d_2)$ distance.

Time $t=\frac{2(d_1+d_2)}{v_s}t=\frac{2(0.3v_s+0.4v_s)}{v_s}t=1.4s$

Hence option 'B' is correct.