Mechanical wave and Law of conservation of energy According to the LCE, energy can not created or destroyed, so during a mechanical wave, why does the wave stop moving? For example, when you drop a rock in the water, the kinetic energy from the rock transforms into the water's kinetic energy and sound energy, but then after that, the wave eventually stops moving. So, where does the energy from the wave go? 
 A: If you can't tell where the energy is going, it's usually heat.
There was once a famous experiment to measure the "mechanical equivalent of heat". A weight was used to pull on a string which rotated a stirrer in a container of water. The temperature of the water was measured before and after the experiment, after the weight had hit the ground and the water had stopped moving. The experimenter found that the mechanical energy from the weight had been converted into heat.
A: When you drop a rock into water, some of the rock's kinetic energy is turned into sound waves (the "splash" sound), some of which propagate into the air and some into the water. Both media possess viscosity and so the acoustic energy in the sound waves eventually is converted into (a tiny amount of) heat.
Some of the rock's kinetic energy is converted into gravity waves (big ripples) that radiate away from the drop point. Some of it is converted into capillary waves (tiny ripples) which also propagate away. Here again, viscosity in the water eventually damps out the wave motion and converts it into heat too.
As the rock continues to fall down through the water, friction between the rock and the water surrounding it causes the rock to share its velocity with the water closest to it, which acts to slow down the rock and to set the water in motion, creating a wake behind the rock. viscosity dissipates the wake, turning its kinetic energy of motion into heat.
Eventually the rock hits the bottom and gets stuck in the mud. The mud has lots of viscosity and easily absorbs the remainder of the rock's kinetic energy, bringing the rock to a halt and warming up the mud a little bit.
