Sound Intensity and Distance: Exploring the Limits of Human Hearing

[hartraft]

1. If the human ear can detect sound of an intensity of 10$$^{-12}$$ given a power source of 50W what is the maximum distance the sound could theoretically be heard



2. I = $$\frac{P}{A}$$

A = 4$$\pi$$r$$^{2}$$



3. Just used first equation to get the area and from that the radius and therefore distance. Thought this was a really standard inverse square law question ( i still think it is). My problem is the answer I get. A distance of 1994.7 km or 1994711.402 metres. This seems mad. I worked out what the decibel equivalent of this power is and it came out to be around 136 dB. This is quieter than a jet engine. This would mean i could hear planes from Scotland by standing in cornwall given perfect conditions. Is this right

 

[Redbelly98]

Welcome to Physics Forums Your answer is correct, though I would be careful with the significant figures.

I agree that this result seems pretty fantastic. Some possible explanations why this doesn't seem to happen are:

1. Normally many things around us produce noise louder than 10^-12 W/m², in which case we would not notice sound of this level.
2. Sound gets absorbed due to air friction, so that over this distance it is actually weaker than what the inverse-square-law says.
3. Often, there could be some obstruction between yourself and something this far away: trees, hills, or buildings, for example. This would affect the intensity of the sound when it reaches you.

 

[hartraft]

Thanks very much for the reply, that has put my mind to rest. I understood that the question was implying perfect conditions which could never be met, but the answer was such a surprise to me I wasn't sure to believe it. Now it's confirmed.

Thanks again