Question

two earthquake waves of the same frequency travel through the same portion of the earth, but the second is carrying 6.0 times the energy of the first. part a what is the ratio of the amplitudes of the two waves? express your answer using two significant figures. a2/a1 =

Explanation:

Step1: Recall energy - amplitude relation

The energy $E$ of a wave is proportional to the square of its amplitude $A$, i.e., $E\propto A^{2}$. So, $E_1 = kA_1^{2}$ and $E_2=kA_2^{2}$, where $k$ is a proportionality constant.

Step2: Find the ratio of amplitudes

We know that $E_2 = 6.0E_1$. Substituting $E_1 = kA_1^{2}$ and $E_2=kA_2^{2}$ into $E_2 = 6.0E_1$, we get $kA_2^{2}=6.0kA_1^{2}$. Canceling out the $k$ on both sides, we have $\frac{A_2^{2}}{A_1^{2}}=6.0$. Then, taking the square - root of both sides, $\frac{A_2}{A_1}=\sqrt{6.0}\approx2.4$.

Answer:

$2.4$