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

[AlecYates]

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).

 

[pbuk]

They are not asking for the amplitude at each site, they are asking for the ratio of the amplitudes A1/A2.

 

[AlecYates]

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?

 

[Redbelly98]

So the ratio of the wave amplitudes is 1.78. Can anyone confirm or refute this?

Yes . . . you yourself can confirm or refute this

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?

 

[AlecYates]

Ah yes that makes sense. Cheers.