Logs

PeterMount

New member
Please find attached a dB (intensity of sound) question that uses a Log scale. Please could someone solve this for me.
With thanks
PeterMount

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Staff member

PeterMount

New member
Subhotosh, it is not an assignment, it is just one question that a few people have approached in different ways. I want to see how others would approach the solution, rather than giving them a hint. It is not too onerous.

Dr.Peterson

Elite Member
For the sake of those who don't want to open a pdf, here is the question, which is no trouble to type in:

If dB = 10log_10(P*10^16), where dB is the intensity of sound in decibels, and P is the power of the sound in watts/cm^2, what is the effect on P when dB is increased by a factor of 3?​

Yes, there are several ways to do this; it would be helpful if you followed the guidelines, if only by stating the context initially.

My suggestion to you would be to replace dB in the equation with 3dB (which is what "increased by a factor of 3" means), and solve for P. This is the best way for someone who has never seen such a problem before, as it will help in understanding. There are other ways to do it if you have various levels of familiarity with the problem.

PeterMount

New member
There actually was no other context stated, this is the question as put, and the only context is around where dB and P are defined as above as following the guidelines. It was amongst other log questions, and does not follow any other context. I have given as much as I can or know.

So when dB is replaced by 3dB how do you progress from there given it is a logarithmic scale?

JeffM

Elite Member
I would solve the original equation for p. Then replace d (for decibel) with 3d and take the ratio of the two p values.

• Jomo

Dr.Peterson

Elite Member
There actually was no other context stated, this is the question as put, and the only context is around where dB and P are defined as above as following the guidelines. It was amongst other log questions, and does not follow any other context. I have given as much as I can or know.

So when dB is replaced by 3dB how do you progress from there given it is a logarithmic scale?
The "context" I referred to was your context, which you provided subsequently: "It is not an assignment, it is just one question that a few people have approached in different ways. I want to see how others would approach the solution ." In the guidelines summary, we ask you to tell us where a problem comes from, and what questions you have about it, so we know what sort of help you need. In this case, you were looking for alternative solutions.

On the other hand, it appears that you don't have a solution, but are in fact asking how to proceed. That has been answered in part by JeffM (and in part by what I said). If you are having trouble carrying this out, it would be appropriate to show what steps you have tried. I will tell you that this problem is a good example where you just have to start doing something without being sure where you will end up -- a little boldness is needed. If you try solving for P, you will eventually discover what kind of answer can be given (which turns out to be a ratio, but you may not know that until you work through it).

So, please give it a try. Following JeffM's approach, you have d = 10log_10(P*10^16) ; how can you start to isolate P? You might first divide both sides by 10; then undo the logarithm in any of several ways (generally involving its inverse, an exponential function), and continue from there. Presumably you have learned how to solve log equations; this may have a different feel than others you've done, so let us know where questions arise as you work on it.

• JeffM