A ripple is created in water. The amplitude at a distance of 5 cm from the point where the sound ripple was created is 4 cm. Ignoring damping, what will be the amplitude at the distance of 10 cm ?
For simplicity let's assume that the ripple was created in a pool of water at the center so that with time the ripple expands on all sides unhindered.
Let the energy of the ripple be
At a distance of
The energy has been distributed in a circle of radius
Hence per unit energy,
When the ripple reaches a distance of
Dividing the two expressions we obtain
We observe that per unit energy is reduced by
We know that energy is directly proportional to the square of the Amplitude of the ripple.
Since damping is to be ignored and assuming ripple to be perfect, the amplitude should decrease by a factor of
Hence requisite amplitude