Answer to Question #254805 in Physics for jay

Question

Two earthquake waves of the same frequency travel through the same portion of the Earth, but one is

carrying 3.0 times the energy. What is the ratio of the amplitudes of the two waves?

Answer 1

The energy of the waves is proportional to their amplitedes squared. Let $E_1, E_2$ be the energies of the two waves, and $A_1,A_2$ be their amplitudes. Thus, have:

$$\dfrac{E_2}{E_1} = 3$$

One the other hand:

$$\dfrac{E_2}{E_1} = \dfrac{A_2^2}{A_1^2} = 3$$

Taking the square root, find:

$$\dfrac{A_2}{A_1} = \sqrt{3}$$

Answer. The ratio of the amplitudes of the two waves is $\sqrt{3}$.