Question

A stone is thrown in a pool of water. The amplitude of waves falls of with distance 'r' from impact point as?

a. 1 / r^1.5

b. 1 / r^2

c. 1 / r^0.5

d. 1 / r^3

the answer is c, please explain to me

Answer 1

When the waves are formed, the intensity of waves decreases with distance from the source. Also, intensity is proportional to square of amplitude where amplitude also decreases with time.

The amplitude of wave depends on wave energy. More wave energy,more amplitude.

We know that energy is directly proportional to the square of the Amplitude of the wave

E∝A²

Since damping is to be ignored and assuming wave to be perfect, the amplitude should decrease by a factor of 1/√r

Therefore the answer is 1/r^0.5.