## anonymous one year ago The amplitude of a wave is A and intensity is I. Which amplitude is neccessary for the intensity to be doubled to 2I? a. A^2 b. √A c.√2A d. 2A

1. Michele_Laino

the intensity is proportional to the square of the amplitude

2. anonymous

I=kA^2 so i multiplied both sides by two to get 2I=2A^2 am i right?

3. Michele_Laino

yes! correct! So, the new amplitude is: sqrt(2)*A

4. anonymous

But wouldn't it give √2I too? Or it doesn't matter ?

5. Michele_Laino

no the intensity is 2*I, so we can write: $2I = K{A^2} + K{A^2} = 2K{A^2} = K{\left( {\sqrt 2 A} \right)^2}$

6. Michele_Laino

so the new amplitude is: ${\sqrt 2 A}$

7. anonymous

But if we square root one side of the equation won't we do the same to the other side? So it becomes like √2I=k√2A ?

8. anonymous

@Michele_Laino

9. Michele_Laino

I haven't squared root the sides of that equation. The new intensity is 2*I, and as all intensities, it has to be proportional to the square of some amplitude, so I can write: $\Large 2I = K{B^2}$ where B is the new amplitude. Now comparing that equation with the previous equation: $\Large 2I = 2K{A^2}$ we can write: $\Large {B^2} = 2{A^2}$ and taking the square root, we get: $\Large B = \sqrt 2 A$

10. Michele_Laino

@rosestella

11. anonymous

Ohh! I get it if you put √2A in 2I=kB^2 you get 2A^2 THANKYOU SO MUCH !!!!

12. Michele_Laino

:):)