What is the ratio of the amplitudes of the two waves?

AI Thread Summary
The discussion centers on calculating the ratio of amplitudes of two earthquake waves with different energy levels. The intensity of a wave is proportional to the square of its amplitude, represented by the equation I = A^2. Given that one wave carries ten times the energy of the other, the intensity ratio is I1 = 10 * I2. Consequently, the amplitude ratio is derived as the square root of the intensity ratio, resulting in a value of approximately 3.16. This indicates that the amplitude of the wave carrying more energy is about 3.16 times greater than that of the other wave.
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Homework Statement



Two earthquake waves of the same frequency travel through the same portion of the Earth, but one is carrying ten times the energy. What is the ratio of the amplitudes of the two waves?

Homework Equations



I=Intensity
A=Amplitude
P=Power

I=A^2


The Attempt at a Solution

 
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You have already written the right eqn, I=A^2.

I1 = 10*I2.
 
I=10

10=A^2

SquareRoot(10)=A

A=3.16
 
Correct.

A better way to write it would be: reqd ratio = sqrt(ratio of intensities) = sqrt(10) = 3.16.
 

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