Heres the source fo this: http://www.naturealmanac.com/archive/beaver_dams/beaver_dams.html

Make of it what you will, there is no attribution to "Researchers" or "The Grad Student's" name is not attached.

"This fact has been scientifically proven - and for most people this explains why beavers build dams. What else would a giant hyperactive stream dwelling aquatic rodent do to release all that busy- ness? But does this explain the beaver's odd behavior?

Otters, too, are busy, and they also live in streams, as do mink and muskrats and even some species of shrews and moles. Yet only beavers build dams. Fortunately there are people around who find this compulsive dam building behavior of beavers as troubling as I do and they decided to find out exactly why the beaver builds his dam.

Humans have always marveled at the beaver's ingenuity since he always picks the narrowest part of the stream for the site of his dam. This fact was always cited as proof of the beaver's intelligence and engineering skill. Yet even a modest acquaintance with beavers will soon reveal that they are far from cunning beasts. It was at this stage of the debate that a young grad student entered the scene and began to investigate.

He noted that beavers living in ponds and lakes and along rivers never build dams - so this compulsive beaver barrier building business was not a result of their busy nature since non-dam building beavers found an outlet for their busy-ness in some way other than dam building. He therefore obtained several pairs of beavers (all with proven dam building track records), released them in different environments and then sat back and watched what they did.

Those released in ponds and large rivers burrowed into the bank, set up beaver housekeeping and then showed no more desire to construct anything beyond their holes. Those released along streams, however, found likely looking pools and then proceeded to deepen them by constructing dams at the narrow, shallow, downstream end. This set the investigator to thinking...

So he proceeded to a riffle (the shallow, high gradient part of the stream) and set up a tape recorder to tape the sound of the water rushing over the gravel and stones. He then set up speakers around known beaver haunts and at dusk turned the tape on.

Lo and behold when he returned the next morning he found the speakers buried under several feet of sticks, gravel and mud - thus effectively silencing the sound. The result was the same whether done along a beaver dammed stream, a large (and quiet) river or a lake or pond. The beavers always covered the speakers until they couldn't hear the sound of rushing water.

And the mystery was neatly solved! Based on experiments with both free living and captive beavers the researcher found that the sound of rushing water was as annoying to a beaver as the sound of fingernails on a blackboard is to humans. And that beavers will pile up sticks and mud in any spot they hear that sound until they can no longer hear it.

This explains in one go why beavers always pick the narrowest and most shallow section of stream to build their dams - it's because that's where the noise is. And they continue piling up sticks and mud in that spot until that annoying sound is silenced. In short, beavers build dams because they like peace and quiet."

tldr: beavers build dams to silence the noise of the running water over rocks.