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?
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This is Giancoli Answers with Mr. Dychko. The energy transported by a wave is 1/2 times some effective spring constant times amplitude squared. And this k effective spring constant depends on what the material is and the only important thing for us is to know that the k is the same for the 2 waves because they go through the same material. And so we can take the ratio of these energies and we have 1/2 kA amplitude 2 squared divided by 1/2 k amplitude 1 squared and the 1/2 k's cancel. And we can solve for the ratio of amplitudes then by taking the square root of both sides and we get A2 over A1 is square root of E2 over E1. And we're told that one of the waves carries 5 times the energy of the other. So, we'll say E2 is 5 times E1 which case E1's cancel giving square root 5 is the ratio of the amplitudes. And so the higher energy wave will have an amplitude 2.2 times greater. And then the lower energy wave.
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