Amplitude and intensity of rock concert

[L1988]

Homework Statement

At a rock concert, the engineer decides that the music isn't loud enough. He turns up the amplifiers so that the amplitude of the sound, where you're sitting, increases by 87.0%. By what percentage does the intensity increase? Do not enter unit.

Homework Equations

I used the fact that intensity is proportional to amplitude squared.

(A2/A1)^2 = I2/I1

The Attempt at a Solution

85% increase in A, so:

(1.85)^2=I2/I1

3.4225=I2/I1

I2=3.4225I1

3.4225x100= 342%

342%-100% = 242%

Answer=242 <-- which is incorrect.

where did I make my mistake?

 

[astrorob]

Hey there,

For a start is it 87% or 85%?

..increases by 87.0%

..85% increase in A, so:

 

[caleb20k]

the problem is that you didn't compute the percent by using a percent difference. All of your work is right but you need to use (I1-I2)/I1 = percent difference, use this instead of a straight fraction like you calculated. if you use this equation you will get the desired answer.