Normally, if you hear a sound, you have some idea of where the sound came from. But when a scuba diver hears a sound underwater, it is virtually impossible to tell where it came from.

1. Why?

2. Can you suggest some form of underwater hearing aid type device that would allow more accurate underwater sound localization?

In a plane, the set of all points the ratio of whose distances from two points (such as idealized ears) is a constant (being the square root of the ratio of the sound volumes) is a circle, sometimes called the circle of Apollonius, but that term is also used for other types of circles.

The set of all points on a plane the difference of whose distances from the two points is a constant (judged by the difference in times that the sound is heard), is a hyperbola.  The circle and the hyperbola meet at two points.  In three-dimensional space, this would rotate about the ear-to-ear axis and localize a sound on a circle perpendicular to the ear-to-ear axis, except that the shape of the external ear and the need for the sound to go around the head would distort the actual localization, but presumably the brain has learned by experience the correlations of location vs. time delay and relative volume.

The speed of sound in 20-degree-Celsius air is about 344 meters per second, while in water it's about 1482 meters per second, or about 4.3 times as fast.  If the ears are 0.2 meters apart, the delay from one side to the other is at least 1/1720 seconds in air when the source is directly right or left (actually more since the sound has to go around the head). In water, the equivalent figure would be 1/7396 of a second.

I would think that in water as in air, the inverse square law would work and there would be less problem with the volume-ratio portion of the direction cues.

An electronic solution would be to have separate microphones feed sounds into a processor that would have to correlate the identity of sounds heard in the two ears up to about a time difference of about 1/7000 of a second, determine the actual time interval between them, and delay the second sound by an additional 3.3 times the measured interval, to play back in the corresponding ear.

A less technological but more obtrusive way would be to have microphones at the end of stalks about a foot long (or about .1 * 3.3 meters) on either side of the head feeding into their corresponding ears.

Posted by Charlie on 2005-04-14 13:35:30