Question

A man standing in front of a vertical cliff fires a gun and hears the echo after 4 seconds. He moves 175 m towards the cliff and fires the gun again. This time, he hears the echo after 3 seconds. Find the correct statement(s).

Note: Question can have mutliple correct options

[2 marks]

• A. The distance between the initial position of the man and the cliff is 700 m.
• B. Speed of sound is 350 m/s.
• C. Speed of sound is 320 m/s.
• D. The distance between the initial position of the man and the cliff is 350 m.

Answer 1

Answer: (A), (B)

Speed of sound is 350 m/s.

Given,
Time to hear the first echo, $t_1$ = 4 s
Time to hear the second echo, $t_2$= 3 s
Distance between the first and second source locations, s = 175 m

Let the distance of the cliff from the first location be d.
Let the speed of sound be v.

Since echo is a reflection of the original sound, it will travel distance equal to twice the distance between man and cliff, i.e., 2d.
From the definition of speed,
$v=\frac{2d}{t_1}$ ...........(i)

Now, after travelling 175 m towards the cliff, the distance travelled by sound,
$d_2=2(d-175)=2d-350$

Again, from the definition of speed,
$v=\frac{2d-350}{t_2}$ ................(ii)

Equating the value of v from equations (i) and (ii), we get,
$\frac{2d-350}{t_2}=\frac{2d}{t_1}\frac{2d-350}{3}=\frac{2d}{4}$

Solving the equation, we get,
d = 700 m

And v =$\frac{2d}{t_1}$

= $\frac{2\times 700}{4}m/s$

= 350 m/s

Hence, the distance between the initial position of the man and the cliff is 700 m, and the speed of sound is 350 m/s.