Wave amplitude and energy spreading · BPhO 2009 #9
Physics
Problem
A wave on the surface of a liquid has amplitude A when it is emitted from the source of the wave, which is a dipper moving up and down in the liquid. The wave spreads out over the plane surface of the liquid, forming a circle of radius r which increases at the speed of the wave.
The energy of the wave is spread out over the circumference of the circle, so that as the circumference increases, the energy in a unit length of the circumference decreases as 1/r. If the energy of the wave is proportional to the square of its amplitude A, then what is the new amplitude of the wave when r increases by four times from its previous value?
A. A/2
B. A/4
C. A/8
D. A/16