# Ratio of wave amplitudes

1. Jul 26, 2014

### AlecYates

1. The problem statement, all variables and given/known data
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?

2. Relevant 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)

3. 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).

2. Jul 26, 2014

### MrAnchovy

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

3. Jul 26, 2014

### 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?

4. Jul 27, 2014

### Redbelly98

Staff Emeritus
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?

5. Jul 27, 2014

### AlecYates

Ah yes that makes sense. Cheers.