What is the ratio of wave amplitudes at two sites with 5dB attenuation?

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Discussion Overview

The discussion revolves around a homework problem concerning the calculation of the ratio of wave amplitudes at two seismic recording sites that experience a 5dB attenuation. Participants explore the relationship between power and amplitude in the context of decibel measurements.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant outlines the problem and expresses confusion regarding the calculation of amplitude ratios based on the given dB attenuation.
  • Another participant clarifies that the question specifically asks for the ratio of amplitudes A1/A2, not the individual amplitudes.
  • A participant calculates the power ratio corresponding to the 5dB change, arriving at a value of 3.16, and subsequently determines the amplitude ratio to be approximately 1.78.
  • Another participant prompts the original poster to verify their calculation by checking if the ratio of 1.78 yields a 5dB difference when applied to the dB formula.

Areas of Agreement / Disagreement

Participants generally agree on the method to find the amplitude ratio from the dB change, but there is no consensus on the correctness of the calculated ratio of 1.78, as verification is suggested but not completed.

Contextual Notes

The discussion does not resolve whether the calculated ratio is correct, as participants do not perform the final verification step.

AlecYates
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Homework Statement


Doing my own independent study, and I've come across a textbook question I'm rather lost on.

Problem: Over the distance between two seismic recording sites at different ranges from a seismic source, seismic waves have been attenuated by 5dB. What is the ratio of the wave amplitudes observed at the two sites?

Homework Equations



From what I can gather, the chapter offers:

The ratio of two power values P1 and P2 is:

10log(P1/P2) dB

Which also gives:

20log(A1/A2) (as power is proportional to the square of signal amp A)

The Attempt at a Solution



This is where it all seems to go wrong with no real idea what direction I should be taking, this may be due to a lack of understanding somewhere.

Given that the waves have decreased by 5dB between site A and B i went with:

20log(A1) = x (1)
20log(A2) = x - 5 (2)

With A1 being the amplitude at site A and A2 being the amplitude at site B. This didn't seem to get me anywhere though as even after subbing 1 into two, i still have two unknown variables to find.

Any help would be appreciated. I don't necessarily need a full answer but a little guidance as to whether I've understood the question wrong i.e. they're not asking for the amplitude at each site, or whether my method is completely off (or both).
 
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They are not asking for the amplitude at each site, they are asking for the ratio of the amplitudes A1/A2.
 
Okay sweet, so this is where I'm at (there are no solutions provided unfortunately).

The change in dB between site A and site B is 5dB.

A change in power ratio by a factor of 10 corresponds to a change of 10dB. Therefore the power ratio would be 10^(5/10) = 3.16 (2.d.p)

since P = A^2 the ratio of the two amplitudes at site A and B would be the root of this answer, so 1.78 (2.d.p).

So the ratio of the wave amplitudes is 1.78. Can anyone confirm or refute this?
 
AlecYates said:
So the ratio of the wave amplitudes is 1.78. Can anyone confirm or refute this?
Yes . . . you yourself can confirm or refute this :smile:

Since you (correctly) said that dB, in terms of amplitudes, is 20log(A1/A2), do you get a result of 5 when you set A1/A2 equal to 1.78?
 
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Ah yes that makes sense. Cheers.
 

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