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 and your GPS receiver is not working. 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 a short blast of sound at a pitch of 120 Hz every 2.00 seconds 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 1.7 kilometers 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 minutes at a speed of 8.8 kilometers per hour (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 the "honks" as if they were wave crests). (Hint: the answer is about 16 kilometers)
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 and your GPS receiver is not working. 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 a short blast of sound at a pitch of 120 Hz every 2.00 seconds 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 1.7 kilometers 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 minutes at a speed of 8.8 kilometers per hour (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 the "honks" as if they were wave crests).
(Hint: the answer is about 16 kilometers)
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