Physics Question

Question

A boat is floating at rest in dense fog near a large cliff. The captain sounds a horn at water level and the sound travels through the salt water (1470 m/s) and the air (340 m/s) simultaneously. The echo in the water (due to the cliff) takes 0.40 s to return. How much additional time will it take for the echo in the air to return?

Answer 1

The distance that both soundwaves have to cover is the same (to the cliff and back).

(1) Δx_sw = Δx_air

Since there is no information about it, we simply neglect anything that could have an effect on the speed or path of sound in these two mediums (no wind, no temperature gradient,...).

The soundwaves move with a constant speed:

(2) Δx_sw = v_sw*t_sw

(3) Δx_air = v_air*t_air

The physics part here is done, now it is an algebra problem. I am not going into detail here, try it yourself. Let me know if you get stuck.

The question is to find Δt = t_air - t_sw

Using the equations above:

Δt = [ (v_sw / v_air) - 1 ] * t_sw

Δt ≈ 1.3 s (rounded to two significant figures)