Sound travelling along straight lines would disperse quickly into the space above the lake.  Instead, sound that "should" rise up and be lost, typically curves back down to the lake/ground level.  Therefore, it sounds louder than it "should.".  This is a well-known and easily demonstrated observation, measurable out there on real lakes.  See, for example, "Powerboat Sound Level Engineering Report", by the National Marine Manufacturers Association, 10/16/87.

In general, air varies in temperature from the surface of a lake (or the ground) on upwards.  On a typical sunny summer day, the air is coldest near the lake's surface.  The air temperature increases as you rise above the lake. This is because the lake water is colder than the air; the air heats up quickly in the day's sunshine.  Also, it's because of the cooling that takes place with water evaporation at the lake surface.  This air temperature pattern is called a "thermal inversion".

Consider a source of sound on a lake, say a jet ski noisily "whomping" along.  A thermal inversion causes the sound generated by the jet ski to stay near the lake's surface.  According to "Fermat's Principle of Least Time" (or an acoustics/optics version called "Snell's Law of Refraction"), this sound curves back down towards the lake surface, and does not disperse much into the space above. 

Other explanatory factors contributing to sound's all-too-good transmission over water may include reflection off the lake surface or underwater conduction of sound.  Whatever the explanation, the most important fact is that experimental measurements demonstrate it to be true.

The speed of sound is not constant; it travels faster in warmer air than in cooler air.  (The speed  is roughly proportional to the square root of the absolute air temperature).  If a bit of sound "wanted" to travel from one spot on a lake (say, the jet ski) to another spot on the lake (say, a frustrated would-be enjoyer of a quiet lake), it could travel on a straight line along the lake surface.  However, this sound could get there faster by rising up to a higher level where the air is warmer (where it could travel faster), then travel parallel to the lake surface but at that higher level (and therefore faster), and finally descend back to the lake surface and the would-be enjoyer.  Even though this roundabout route would be a bit longer in distance, it would take less time, due to the faster speed of sound at the higher level. 

As bizarre as it seems, sound (and similarly, light) travels, not along straight lines, but along whatever  path gets it there the fastest, even a curved path.  This is called "Fermat's Principle of Least Time."  It states that sound always takes the path that gets it there fastest, that is, in the "least time."  This seems very strange; one should wonder, "How does sound KNOW how to do this?  How does sound KNOW what lies ahead of it along different paths?"  Well, somehow it does, and much deeper physics explains why ("stationary phase"), but we'd better not go there now.

Consider this analogy.  A person wants to wade in the water near a beach, from one place to another, at both of which the water is waist-deep.  (Assume that the two places are relatively far apart from each other.) He could travel in a straight line (through the waist-deep water), but he could get there faster if he contoured into shallower water (where he could travel much faster) for most of his journey.  However, this requires some planning and understanding on the part of the wader, and it's really not clear how a bit of sound can do this sort of planning.  But somehow, it can and does.  (Physics just gets weirder and weirder, the deeper you go.  In modern quantum mechanics, particles often behave "as if they were conscious", but of course, they're not ... we think.)

The opposite situation holds in a desert.  The air is hottest near the ground, and is cooler higher up.  Thus sound travels faster near the ground, and slower higher up.  The Principle of Least Time predicts that sound will curve upwards in a desert.  Consequently, sound dies away rapidly with distance in a hot (desert) environment.  This explains why it's very quiet in a desert;  the sound curves upwards into space, and is not heard by the observer on the ground.

Light also obeys Fermat's Principle of Least Time, and light also travels faster in hot air than in cold air.  (This is for a different reason, but that's not important here.)  So, light curves upwards in a desert, or over a hot dry highway, giving rise to the well-known "mirage" phenomenon.  (See the top illustration in "Refraction/Snell's Law".) 

For further evidence that light doesn't necessarily travel in a straight line, look over a bonfire, and notice the little visual wiggles in what you see on the other side.  This is due to small pockets of hot air rising from the fire, mixing chaotically with the colder air.  Or notice the "bend" that light seems to take when it moves across an air-to-glass boundary; light travels much faster in air than in glass.  Lenses (and eyeglasses) work by this principle.  Similarly, light travels much faster in air than in water.  Next time you fill a transparent tumbler with your favorite beverage, pause for a moment to observe the Principle of Least Time in action.  Cheers!

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Howard Shaw, Ph. D.

Cheryl Jackson Hall, Ph. D.

P.O. Box 1275

Gunnison, CO 81230-1275

Phone: (970) 641-1440

E-mail: hallshaw@gunnison.com

or HShaw@alum.mit.edu