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

In summary, the conversation is about a question regarding the ratio of amplitudes observed at two different seismic recording sites. The textbook offers equations for calculating the ratio of power values and amplitude values. The person asking for help tries to solve the problem by setting up equations for the amplitudes at each site, but is unsure if they are on the right track. Another person confirms that the ratio of the amplitudes is 1.78.
  • #1
AlecYates
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0

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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  • #2
They are not asking for the amplitude at each site, they are asking for the ratio of the amplitudes A1/A2.
 
  • #3
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
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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  • #5
Ah yes that makes sense. Cheers.
 

1. What is the ratio of wave amplitudes?

The ratio of wave amplitudes refers to the comparison of the heights or magnitudes of two different waves. It is calculated by dividing the amplitude of one wave by the amplitude of the other wave.

2. How is the ratio of wave amplitudes used in science?

The ratio of wave amplitudes is used in various fields of science, such as physics, engineering, and astronomy. It can help determine the strength of a signal or the intensity of an event, and it is also used in analyzing and understanding wave phenomena.

3. What factors can affect the ratio of wave amplitudes?

The ratio of wave amplitudes can be affected by various factors, including the properties of the medium through which the waves are traveling, the distance between the waves, and the characteristics of the sources of the waves.

4. How is the ratio of wave amplitudes related to wave interference?

The ratio of wave amplitudes plays a crucial role in wave interference, which is the phenomenon of two or more waves combining to form a resultant wave. The ratio of amplitudes determines the type and strength of interference that occurs.

5. Can the ratio of wave amplitudes be used to compare waves of different types?

Yes, the ratio of wave amplitudes can be used to compare waves of different types, as long as they are traveling through the same medium. This is because the ratio is a unitless quantity that only considers the relative magnitudes of the waves, regardless of their physical properties or units of measurement.

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