# Intensity of sound, power output

jangchen
Homework Statement:
A loudspeaker, mounted on a tall pole, is engineered to emit 75% of its sound energy into the forward hemisphere, 25% toward the back. You measure an 85 dB sound intensity level when standing 3.5 m in front of and 2.5 m below the speaker. What is the speaker’s power output?
Relevant Equations:
dB = 10 log(I / Io) , I = P / 4pi×r^2
I is proportionate to E.

r = 4.3xxm

So I put 0.75I

But I got 97.xxmW

What is wrong?

Homework Helper
Gold Member
I get 49 mW. If you show the details of your calculation we can maybe spot a mistake. If I had to guess, I would say you used 4πr2 for the area of a hemisphere.

• jangchen
Homework Helper
Your equation for I assumes the energy distribution is spherically symmetrical. But the question tells you that is not true. If 75% of the energy is emitted forwards (as opposed to 50% for spherical symmetry), how would that affect the I value you measure?

jangchen
If I had to guess, I would say you used 4πr2 for the area of a hemisphere.
Oh, I used 4πr2.. Do I have to use 2πr2 ?

Homework Helper
If 75% rather than 50% of the energy goes forwards, then
Iforward = 1.5P/4πr2
I'm not sure what you meant by "So I put 0.75I", but if it means you used 0.75 instead of 1.5 in the above equation, then that would explain your error.

Homework Helper
Gold Member
There's more than one way to think about it. Can you answer each of the following?
(1) What is the intensity I (in W/m2) at the point given?
(2) What is the total power P (in W) of sound radiated in the forward direction (hemisphere)?
(3) How is the answer to (2) related to the total power radiated by the speaker?

jangchen
Now I understand surely. Thank you!