Question

A person standing between two vertical cliffs and 640m away from the nearest cliff shouted. He heard the first echo after 4 seconds and the second echo 3 seconds later. Calculate the distance between the cliffs.

• A. 176 m
• B. 1700 m
• C. 1760 m
• D. 1800 m

Answer 1

The correct option is C. 1760 m

Let the person be standing 640 metres away from Cliff A. It is given that the person shouted and he heard the echo after 4 seconds. When the person will shout, the sound waves will go from the person to Cliff A and return to him again. This means the sound waves travel a distance of 640 metres two times. Therefore the total distance travelled by the sound is

$d=640\times 2=1280m$.

This distance is travelled by sound in 4 seconds. So the speed of the sound is

$v=\frac{1280}{4}=320m/s$.

This speed of sound is constant.

Let the second echo strike the other cliff, say Cliff B. The time taken by the echo to return to the person is 4 + 3 = 7 seconds.

Since the speed of sound is 320 m/s, the total distance travelled by the sound waves is

$d^{\prime }=320\times 7=2240m$.

But this is the total distance travelled by the sound waves, which will be two times the actual distance between the cliff and the person.

Therefore, the distance between the cliff and the person will be 2240/2 = 1120 m. So, we obtain two equations —

Distance between the person and Cliff A = 640 m.

Distance between the person and cliff B = 1120 m.

Therefore the distance between the two cliffs will be 640+1120 = 1760 m.