Consider a spherical waves emanating from a point source initially having the amplitude is $A$. As he wave travels, forming wavefronts, will the amplitude of each point in all the secondary wavelets be the same? The new wavefront will surely have a larger size. So will each point in this wavefront also have the same initial amplitude $A$? If so, isn't it against the law of conservation of energy? Because, initially in a small wavefront less particles were oscillating with amplitude $A$ and after that many more particles are oscillating with the same amplitude $A$. So the energy is increasing as the wave is propagating. If we assume amplitude decreases at successive wavefronts, then won't the wave disappear after certain distance? I have thought about this a lot, but I am not able to figure it out.
Can anybody shed some light on it in detail?
ANY HELP IS GREATLY APPRECIATED
Best Answer
The simple model of wavelets is adapted to take care of two things.
One is your idea that the amplitude of the wavelets must decrease with distance and the is done with a $\frac 1 r$ term where $r$ is the distance the wavelets has travelled. This ties in with the intensity (energy per second per unit area) falling off as $\frac{1}{r^2}$ as intensity is proportional to amplitude squared.
The other factor which is included is that the amplitude of the wave in a direction at an angle $\theta$ to the forward direction is proportional to $1+\cos \theta$. So the amplitude of the wavelets is not the same in all directions and zero in the reverse direction.