A person is standing at the sea shore. An observer on the ship which is anchored in between a vertical cliff and the person on the shore fires a gun. The person on the shore hears two sounds, 2 seconds and 3 seconds after seeing the smoke of the fired gun. If the speed of sound in the air is 320 ms-1 then calculate:
the distance between the observer on the ship and the person on the shore.
Topic: Sound and vibrations
Answer
Given: speed of sound v = 320 m s⁻¹; the first sound is heard 2 s after the flash.
Light reaches the shore effectively instantly, so the smoke marks the moment of firing. The FIRST sound to arrive is the one that travels straight from the ship to the person.
distance = speed × time = 320 × 2 = 640 m
Distance between the ship and the person on the shore = 640 m
Two sounds arrive because there are two paths: the direct one from the ship, and the longer one that goes on to the cliff and reflects back. The shorter path arrives first, so the 2 s reading belongs to the direct sound.
There is no factor of 2 in this part. The sound goes one way only — ship to shore. Halving it to 320 m is the mistake, made by students who have learnt "echo means divide by two" as a rule rather than a reason. The halving belongs only where the sound goes out AND comes back to the same place.