Chapter 11, Problem 14Q

To determine

Give two reasons why circular water waves decrease in amplitude as they travel away from the source.

Answer to Problem 14Q

Solution:

Friction with the static water and the increase of the wave front.

Explanation of Solution

The energy transmitted in a circular wave by the focus to the medium is distributed along the wave fronts. Therefore, as the wave spreads, its amplitude A decreases proportionally to the distance r to the focus as shown

$A\propto \frac{1}{r}$

The wave front expands so the energy gets more spread out (there is less energy available per unit length of the wave). We know that the energy is directly proportional to the square of the amplitude.

There exists molecular friction with the static water, where they will absorb the energy as heat instead of moving. Part of the energy is converted into heat as the various molecules move past each other.