Why is sounds fainter further away?

Answer 1

As the sound wave travels out from the source, the same amount of energy is covering a bigger and bigger area, so there is less energy per square inch. (In particular, less energy in the square inch reaching your eardrum.)

Imagine the energy as a lump of clay. When a sound wave is only 6 inches (15cm) from the source, the clay has to cover the *surface* of a radius 6in ball, and the clay can be clumped on pretty thick. But as the sound travels outward to 60in (= 5ft =~ 150cm), that same amount of clay now has to cover the surface of the much bigger ball, so it will have to be very thin.

Geometry tells us that the surface area of a sphere is proportional to the radius *squared*. This means that as you get twice as far away from a sound, only a *quarter* of the original energy reaches you. If you get ten times further away (like in the example above), then only a *hundredth* of the original energy reaches you.

[The human ear/brain is sensitive though; half the energy doesn't necessarily mean the brain interprets it as half as loud; the ear/brain has more of a logarithmic response: half the energy is like turning the volume knob down one notch; a sixteenth of the energy is like turning it down four notches. Decibels are units that measure the *logarithm* of the energy, which is why they are suitable units for talking about human hearing.]