A multichoice question on intensity

1. May 16, 2010

Charismaztex

1. The problem statement, all variables and given/known data

A plane wave of amplitude A is incident on a surface of area S placed so that it is perpendicular to the direction of travel of the wave. The energy per unit time reaching the surface is E.
The amplitude of the wave is increased to 2 A and the area of the surface is reduced to
0.5 S.

How much energy per unit time reaches this smaller surface?
A) 4E
B) 2E
C) E
D) 0.5E

2. Relevant equations

Answer is B) by the way.

3. The attempt at a solution

I know that intensity is proportional to (aplitude)^2, but right now I'm a little confused.

Charismaztex

2. May 16, 2010

Redbelly98

Staff Emeritus
That's right. So as a first step in thinking about this, what would happen if all they did was to double the amplitude?

3. May 16, 2010

Charismaztex

so the energy would be proportional to (2A)^2=4A^2. The energy would quadruple. I also know that intensity is inversely proportional to the area, so if the area decreases by half, the intensity would increase by a factor of 2. Wouldn't that mean that the energy would increase by a factor of 8?

I think I'm missing something crucial here.

4. May 16, 2010

Redbelly98

Staff Emeritus
You're essentially correct, but a better way to think of it is that intensity is proportional to amplitude^2.

Next hint: Energy per unit time = Intensity x Area.

5. May 16, 2010

Charismaztex

Wait, I think I may have got it. The amplitude doubles so that the intensity quadruples. But intensity= power/time =energy/(time x area S) so E=I x t x S. Hence if when amplitude doubles and surface area halves, E= 4I x t x 0.5S =2I x t x S Hence energy doubles.

6. May 16, 2010

Redbelly98

Staff Emeritus
Yup, you got it.

7. May 16, 2010

Thanks :)