A bell’s sound 100 miles away is physically inaudible even with sail focusing

Evidence

We can now return to the example at the start of this chapter. Is it reasonable that the sound of a bell can travel 100 miles and be heard aboard a ship? One hundred miles is about 160,000 meters, so the drop in decibels from, say 100 m distance from the town square to 160,000 meters is 10 log[(100/160, 000)2] ≈ 64 dB. Suppose we say the bell 100 m away was a loud 95 dB. This becomes only about 30 dB at the ship, certainly masked by the probable 50 to 70 dB ambient noise aboard a ship. If we assume the sails can reflect 30% of the sound energy incident on them, and that they concentrate the sound by a factor of 1000 by focusing (see figure 2.7), we have amplification by a factor of 300 at the focal spot on deck. This 10 log = 25 dB, so that the sound at the focal spot would be 30 + 25 = 55 dB; still very soft and probably inaudible except on a very quiet ship, quieter than most houses today. — Eric J. Heller, Why You Hear What You Hear- An…, 233

Categorization

• QUESTION: Demonstrates the physics that debunks a folk claim — historically, was such a ‘bell heard at sea’ anecdote actually recorded, and if so what explains it?
• SEED: A nice essay angle: using the physics/numeracy of the dB law to debunk legendary claims about sound traveling improbable distances.