Q1.
Sound travels much farther in water than light, and thus, is used for various underwater applications. A sonar signal sent to find the depth of ocean takes 4 s to return. What is the depth of the ocean at that location if the speed of sound in seawater is 1500 m s–1?
Answer
The ocean is 3000 m (3 km) deep at that place.
The 4 s is the time for the signal to go down and come back.
total distance = speed × time = 1500 m s⁻¹ × 4 s = 6000 m
depth = total distance ÷ 2 = 6000 m ÷ 2 = 3000 m = 3 km
total distance = speed × time = 1500 m s⁻¹ × 4 s = 6000 m
depth = total distance ÷ 2 = 6000 m ÷ 2 = 3000 m = 3 km
Or in one step: d = v t / 2 = (1500 m s⁻¹ × 4 s) / 2 = 3000 m.
Why sonar and not light or radar: water absorbs and scatters light within a few tens of metres, and radio waves are absorbed almost immediately. Sound, on the other hand, travels about 4 – 5 times faster in water than in air and keeps going for kilometres before its intensity falls away. So sound is the only practical probe for the deep sea — which is why ships map the sea floor and find submarines and wrecks with sonar (sound navigation and ranging).
Tip: if a question ever gives you the one-way time instead of the return time, do not halve it. Read carefully whether the time quoted is 'to return', 'for the echo', or 'to reach'.