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

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Homework Help Overview

The problem involves two earthquake waves of the same frequency, where one wave carries ten times the energy of the other. The focus is on determining the ratio of the amplitudes of these two waves.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between intensity and amplitude, referencing the equation I=A^2. There is an exploration of how the intensity ratio relates to the amplitude ratio.

Discussion Status

Some participants confirm the use of the intensity equation and suggest that the ratio of amplitudes can be derived from the square root of the intensity ratio. There is a progression in the discussion towards calculating the amplitude ratio based on the given energy difference.

Contextual Notes

Participants are working within the constraints of the problem statement, which specifies the energy relationship between the two waves but does not provide additional details on the waves' characteristics or the medium through which they travel.

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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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