Distance from sources of different intensity to get same loudness

[coconut62]

Homework Statement

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

Homework Equations

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

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

The Attempt at a Solution

Answer: D

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.

 

[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!

 

[coconut62]

I represents intensity.

 

[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.

 

[rude man]

I represents intensity.

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

 

[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.

 

[rude man]

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.

a-ok!