You are at sea on a foggy night. You are trying to find out how far you are from

Question

You are at sea on a foggy night. You are trying to find out how far you are from the shore, but the fog is too thick to see anything. After a certain time of aimless sailing, you dimly hear two separate foghorns on your port (left) side, perpendicular to your direction of travel. Each foghorn emits one short blast of sound at a pitch of 120 Hz every 2.00 s exactly, and each sounds about as loud as the other. Looking at your map, you see two foghorn locations marked plausibly near what you guess your location to be, and on the map the foghorns are 1700 m apart, flanking the entrance to a harbor. At a certain time, you notice that you hear the blasts from the foghorns simultaneously. After you have sailed at a steady heading for 22 min at a speed of 8.8 km/h (as measured by your boat's speedometer), you hear the foghorns exactly out of phase (one honks, then the other, then the first, etc.). Roughly how far are you from the foghorns now? (Hint: Treat this as a two-slit interference problem.) You are at sea on a foggy night. You are trying to find out how far you are from the shore, but the fog is too thick to see anything. After a certain time of aimless sailing, you dimly hear two separate foghorns on your port (left) side, perpendicular to your direction of travel. Each foghorn emits one short blast of sound at a pitch of 120 Hz every 2.00 s exactly, and each sounds about as loud as the other. Looking at your map, you see two foghorn locations marked plausibly near what you guess your location to be, and on the map the foghorns are 1700 m apart, flanking the entrance to a harbor. At a certain time, you notice that you hear the blasts from the foghorns simultaneously. After you have sailed at a steady heading for 22 min at a speed of 8.8 km/h (as measured by your boat's speedometer), you hear the foghorns exactly out of phase (one honks, then the other, then the first, etc.). Roughly how far are you from the foghorns now? (Hint: Treat this as a two-slit interference problem.) You are at sea on a foggy night. You are trying to find out how far you are from the shore, but the fog is too thick to see anything. After a certain time of aimless sailing, you dimly hear two separate foghorns on your port (left) side, perpendicular to your direction of travel. Each foghorn emits one short blast of sound at a pitch of 120 Hz every 2.00 s exactly, and each sounds about as loud as the other. Looking at your map, you see two foghorn locations marked plausibly near what you guess your location to be, and on the map the foghorns are 1700 m apart, flanking the entrance to a harbor. At a certain time, you notice that you hear the blasts from the foghorns simultaneously. After you have sailed at a steady heading for 22 min at a speed of 8.8 km/h (as measured by your boat's speedometer), you hear the foghorns exactly out of phase (one honks, then the other, then the first, etc.). Roughly how far are you from the foghorns now? (Hint: Treat this as a two-slit interference problem.)

Explanation / Answer

Let first foghorn is at point c and second is at point D.

We are at point B and moving toward BA with velocity 8.8 km/h in time 22min

V = distance/ time

BA = V* t = 8.8*1000*22*60/ 3600 = 3226.6 m

Since velocity of sound is 343 m/s

Distance X = V* t                                    ( frequency = 1/ t, t= 1/120)

X = 343/ 120 = 2.858 m

From Triangle ABC, AC = (BC2 + AB2 )1/2

Our distance from first foghorn AC = 3226.6 m

Simillarly From triangle ABD

Our distance from second foghorn AD = 3648.3 m

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