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?

The term kinetic energy is described as the form of an energy that exists due to the motion of an object.If the object is not moving means the velocity is equal to zero then the value of kinetic energy of the object would be zero.

The given data can be listed below as,

The expression of the kinetic energy of the wave is given by,

\(E = \frac{1}{2}k{A^2}\)

Here,\(E\)is the total mechanical energy of the wave,\(A\)is the amplitude and\(k\)is wave number.

From the above equation, kinetic energy is directly proportional to the square of the amplitude. Hence,

\(\frac{{{E_1}}}{{{E_2}}} = {\left( {\frac{{{A_1}}}{{{A_2}}}} \right)^2}\)

Here, \(\left( {\frac{{{A_1}}}{{{A_2}}}} \right)\) is the ratio of the amplitudes of the two waves.

Substitute all the known values in the above equation.

\(\begin{aligned}{c}\frac{{5{E_2}}}{{{E_2}}} &= {\left( {\frac{{{A_1}}}{{{A_2}}}} \right)^2}\\5 &= {\left( {\frac{{{A_1}}}{{{A_2}}}} \right)^2}\\\frac{{{A_1}}}{{{A_2}}} &= \sqrt 5 \end{aligned}\)

So, the ratio of the amplitudes of the two waves is \(\sqrt 5 \).