Why can we hear a sound with one ear (e.g. the left) when it is actually coming from the direction of the other (e.g. the right)?

• Indeed, if we expose the right ear to light, the left one will be in shadow. So is there no shadow for sound waves?
• There is, but a shadow is a property that depends closely on the wavelength of the waves considered. The closer the size of the obstacles gets to the wavelength, the more blurred the shadow becomes. When the size of the obstacle is comparable to the wavelength of the wave striking it, the shadow no longer exists, and the wave can propagate beyond the obstacle, going around it as if it did not exist at all. This phenomenon is called diffraction. You can see an example by following the instructions on the page diffraction by an obstacle.
• The width of the head (about twenty centimetres) is comparable to the wavelength of many audible sounds. These sounds can therefore go around the obstacle and reach the other ear.
• Of course, for some (high) frequencies the head is a real obstacle, so these frequencies will reach the ear "in shadow" strongly attenuated (they will hardly fail to arrive at all, because the two ears are not completely isolated from each other, and sound can also propagate through the skeleton).
• This means that the spectral content of a complex sound, that is, the intensity of the frequencies that make it up, will be slightly different at the two ears when it comes from one side rather than from the front!

What is the purpose of having two ears?

• The brain can very quickly analyse a great deal of information about an acoustic signal reaching the auditory system. With two ears it can also analyse the difference between two different "perceptions" of the same source. In particular:
  1. a sound coming from the right reaches the right ear slightly earlier than the left.
  2. The signal will be more intense on the right because the head acts as an obstacle for the left ear, especially at high frequencies.
  3. Moreover (see the previous question) the sound reaching the left ear will also have a slightly darker timbre than the one reaching the right ear.
• By processing these differences, the brain can determine information such as the distance and position of the sound source.

Having two ears is roughly the equivalent of having two eyes: it adds the third dimension to the sound field around us. For more details see the page on localisation of the sound source.