Intensity is defined as power per unit area. Show that the decibel level of two

Question

Intensity is defined as power per unit area. Show that the decibel level of two sounds can be related to the ratio of the two powers as dB = 10 log P1/Po
Now, I found some help here but don't understand the answer fully.
I= P/A dB = 10 log I1/Io

intensity of point source
I = P/ 4 pi r^2 so

so I1/Io = (P/4pir^2)/(P/4pir^2) so far so good. Now cancel P, 4, pi. Get that, but then they list (r^2/R^2)^2 where did the second square come from? SO far we think this was a typo!

So now we have delta B = 10 log (r/r)^2 I know the second square was cancelled out by the log but I don't understand how, to equal 20 log r1/r2.
Thanks for the help, it's more the math maneuver here I don't understand, but that is the key to the problem.

Explanation / Answer

B = 10 log (r/r)^2 as the function of log is to take the power behind like B = 10 *2log (r/r) so thats why it became 20 log r1/r2.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.