Solving Sound Wave Confusion: Finding Intensity at Distance d_0 from Source

[HeLLz aNgeL]

Homework Statement

In general, if a sound has intensity of beta dB at 1 m from the source, at what distance d_0 from the source would the decibel level decrease to 0 dB? Since the limit of hearing is 1 dB this would mean you could no longer hear it.
Express the distance in terms of beta. Be careful about your signs!

I know that the relationship between the intensity and distance is an inverse square relationship, but I'm not sure what exactly the question is looking for. Do i have to find the distance when it goes to 0 or to 1 ? Because if that is zero, then even after 100m, the intensity wouldn't be zero ?

im confused !

 

[HeLLz aNgeL]

anyone ?

 

[Dick]

You are right, the intensity won't fall to zero. But there is a log in the relation between dB and intensity.

 

[HeLLz aNgeL]

so how do i get it to zero ? i mean keep on increasing distance till log of it = 0, and how do i write it in terms of beta ? :S

 

[Dick]

Ok, let 'I' be the intensity at 1m and 'I0' be the intensity at 0dB. dB=10*log(I/I0) (all logs base 10). So beta=10*log(I/I0). You know at distance Rm the intensity becomes I/R^2. So 0=10*log((I/I0)/R^2). Now use a property of logs.

 

[TVP45]

Homework Statement

In general, if a sound has intensity of beta dB at 1 m from the source, at what distance d_0 from the source would the decibel level decrease to 0 dB? Since the limit of hearing is 1 dB this would mean you could no longer hear it.

im confused !

Why do you say the limit of hearing is 1 dB?

 

[HeLLz aNgeL]

Ok, let 'I' be the intensity at 1m and 'I0' be the intensity at 0dB. dB=10*log(I/I0) (all logs base 10). So beta=10*log(I/I0). You know at distance Rm the intensity becomes I/R^2. So 0=10*log((I/I0)/R^2). Now use a property of logs.

thanks a ton ! finally got it ... this one was a bugger ! thanks again...