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 cliff and the observer on the ship.
Topic: Sound and vibrations
Answer
Given: v = 320 m s⁻¹; the second sound arrives 3 s after the flash.
From part (i), the ship-to-shore distance is 640 m.
The second sound travels ship → cliff → shore.
total path = 320 × 3 = 960 m
Let the ship-to-cliff distance be d. The shore is on the far side of the ship from the cliff, so this path is d (ship to cliff) + d + 640 (cliff back past the ship to the shore): d + d + 640 = 960 2d = 960 − 640 2d = 320 d = 160 m
Distance between the cliff and the ship = 160 m
Draw the line before you calculate: cliff, then ship, then person, in that order. The second sound goes from the ship up to the cliff, reflects, and comes all the way back past the ship to the person — so it covers the ship-to-cliff gap TWICE plus the 640 m to the shore.
Setting it up as d + 640 = 960 (counting the cliff gap once) gives 320 m, double the right answer. The 2d is what catches people. A sketch with the arrows drawn on it makes the double crossing obvious and is worth thirty seconds.