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

## Question:

Two earthquake waves of the same frequency travel through the same portion of the Earth, but one is carrying 5.0 times the energy. What is the ratio of the amplitudes of the two waves? (Express your answer using two significant figures.)

## Intensity and Energy:

The intensity of a wave directly varies with the power of the wave. As we know that, power is the ratio of energy and time. Thus, the power directly varies with the energy, and energy directly varies with the intensity of the wave. The expression for finding the intensity of a spherical wave is:

{eq}I = \dfrac{P}{{4\pi {r^2}}} {/eq}, where:

• r is the radius of the spherical wave.

We know that power is directly proportional to the energy:

{eq}\begin{align*} P &= \dfrac{E}{t}\;\;\;\;\;\;\;\left( {t = time} \right)\\ P &\propto E\\ P &\propto I \propto E \end{align*} {/eq}

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We are given:

• The ratio of the energy is {eq}{E_1} = 5{E_2} {/eq}

The expression for the energy of the sinusoidal wave is given by:

{eq}E =...