# How far can one hear sound?

I was thinking how far can I hear sound coming from a concert. Today I was walking at night and I could hear sound from somewhere very far. I started following the sound but sound used to disappear momentarily and then reappear. I went atleast 2 miles but could not find where it was coming from.

Now I am really confused because sound is energy and because of energy losses, as I understand sound cannot go as far as 20 miles. The nearest concert was atleast 20 miles away.

I came back and read articles(I cannot proof the reliability) where sound had traveled 200 miles but it was mostly sounds from explosion or volcanoes. Maybe this makes sense because explosions or volcanoes have alot of energy but how can one explain sound being heard from a concert very far away(approx 20 miles).

I think the key here is the question of isotropy of propagation.

The speed of sound in an ideal gas goes as the square root of the temperature. Another way of saying this is that the refractive index for sound waves goes as the inverse square root of temperature. Colder air has a higher refractive index.

At night, it can be the case that the temperature close to the ground is colder than higher up - a temperature inversion. A wave travelling away from the ground will be bent back towards the ground by the decrease in refractive index with height. This (along with the fact it is generally quieter!) can enable you to hear distant events at night.

The threshold of hearing is typically quoted as $I_0 = 10^{-12} W/m^2$ in the literature. This often corresponds to 0 decibels (0 dB).

So, if you're in a wide open space, and a speaker is pumping out audio at X watts (this is not the power your amplifier/speakers consume, but the actual audible power out), then the distance at which that sound will fall to the threshold of hearing is given by:

$$d = \sqrt{\frac{X}{4 \pi I_0}}$$

This assumes that the source is isotropic and that power is conserved (not absorbed as it travels) so that the power per unit area at any distance from the source is the ratio of the total power at the source to the surface area of a sphere with a radius equal to the distance from the source.

In reality, sources aren't isotropic, and sound is damped as it travels. Not to mention trees, walls, etc will absorb and reflect sound, complicating the matter. This equation is more of an upper limit.

There is also a possibility that the sound you heard was from a recording or a broadcast, not from an actual concert.

The 1883 Krakatoa eruption ejected approximately 25 km3 (6 cubic miles) of rock. The cataclysmic explosion was heard 4,800 km (3,000 mi) away in Alice Springs, as well as on the island of Rodrigues near Mauritius, 4,653 km (2,891 mi) to the west.

Taken from Wikipedia.

• The [3] suggests that this is a quote and a quick Google search confirms this (led me to the Wikipedia article on Krakatoa). If you are going to quote something, you ought to include a link to the source and indicate it is a quote by pre-pending > in front of the text. – Kyle Kanos Aug 31 '14 at 20:48