# Can Initial Intensity Differ from Incident Intensity?

• vivekfan
In summary, the equation Beta=10log (I/I (initial)) is used to calculate the difference in sound level between two intensities. The initial intensity should always be the reference intensity of I0 = 10^(-12), but in some cases, such as calculating the difference between two intensities, the initial intensity can be the intensity you were initially at. In the given example of a speaker producing 5W of sound and then increasing to 50W, the level of sound heard would increase from 10 dB to 20 dB. This is because the equation 10log (I/I (initial)) is used to calculate the difference in sound level, and in this case, the initial intensity is 5W and

## Homework Statement

In the equation Beta=10log (I/I (initial)

is the I inital always the incident intensity 10^-12? Or if you are moving from one intensity to another, then can the initial intensity be the one you were initially at? For example, if you were moving from an intensity of 5 to 10, then could the initial be 5 instead of the incident intensity? If so, why?

Given above.

## The Attempt at a Solution

Well, I actually solved a problem in which something went from an initial intensity to a final, and plugged in the initial intensity and got the right answer, but I am confused on why you don't always use incident intensity?

In principle you should always use the reference intensity of I0 = 10^(-12).
However, suppose you want to calculate the difference in sound level when going from intensity Ia to Ib. Then mathematics tells you that

10log( Ia / I0 ) - 10log( Ib / I0 ) = 10log( (Ia / I0) / (Ib / I0) ) = 10log( Ia / Ib )

CompuChip said:
In principle you should always use the reference intensity of I0 = 10^(-12).
However, suppose you want to calculate the difference in sound level when going from intensity Ia to Ib. Then mathematics tells you that

10log( Ia / I0 ) - 10log( Ib / I0 ) = 10log( (Ia / I0) / (Ib / I0) ) = 10log( Ia / Ib )

Well, could you help me work through this problem...

A speaker is producing a total of 5 W of sound, and you hear 10 dB. Someone turns up the
power to 50 W. What level of sound do you hear?
(a) 10 dB, (b) 15 dB, (c) 100 dB, (d) 40 dB, (e) 20 dB

I don't know why I plugged in 50/5 for I and I initial after I used the math function you gave. Please help.