Question

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

Answer 1

the intensity is proportional to the square of the amplitude

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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 ?

Answer 8

@Michele_Laino

Answer 9

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:
\[\Large B = \sqrt 2 A\]

Answer 10

@rosestella

Answer 11

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

Answer 12

:):)