# Distance from sources of different intensity to get same loudness

1. Nov 25, 2013

### coconut62

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

A point source of sound emits energy equally in all directions at a constant rate and a person 8m from the source listens. After a while, the intensity of the source is halved. If the person wishes the sound to seem as loud as before, how far should he be now from the source?

A) 2m B) 2√2m C) 4m D) 4√2m

2. Relevant equations

Intensity (proportional sign) 1/distance$^{2}$

Intensity (proportional sign) amplitude (not sure if needed)

3. The attempt at a solution

I = k/d$^{2}$ , where k is a constant.

I= k/8$^{2}$

k = 64 I

(new I) x (new d$^{2}$) = 64 I

(0.5 I) x new d$^{2}$ = 64I

new d$^{2}$= 128

new d = 8√2 (no answer)

Sounds not very logical, but I don't know how am I wrong. Please explain to me.

2. Nov 25, 2013

### rude man

In your expression I = k/d^2 what symbol represents the intensity of the source?

Your answer is obviously wrong. The naswer has to be < 8m!

3. Nov 25, 2013

### coconut62

I represents intensity.

4. Nov 25, 2013

### nasu

The intensity of the source does not depend on distance from the source.
Review your formulas. You must have one that relates the power emitted by the source with the intensity received at a given distance.

5. Nov 25, 2013

### rude man

No, I represents intensity at the location d. In other words, I = I(d).

6. Nov 26, 2013

### coconut62

I think this is the formula needed:

Intensity = Power/4∏r$^{2}$

So the intensity of the sound where the person stood was P/256∏.

It is now halved. So the power gets halved too.

P= 128∏I

since P = 4∏r$^{2}$I

128∏I=4∏r$^{2}$I

r=4√2

Please correct me if I'm wrong.

7. Nov 26, 2013

a-ok!