At a distance of 14.0 m from a point source, the intensity level is measured to be 80 db. at what distance from the source will the intensity level be 40 db

1400m

Explanation:

For spherical waves we can use the following relationship between distance and intensity:

Where and are the first and second intensity, in . And is the first distance:   , and the distace we want to find.

Clearing the previous equation or

.

This is what we will be using to find the answer, but fist we must convert the quantities 80dB and 40dB to

We will call the quantities in dB and :

We will use the following to find the corresponding intensities and :

for both of these: , and it is the minimum intensity that a human being perceives.

Thus, for we have:

And to eliminate the logarithm, we use its inverse operation, exponentiation.

replacing :

and similarly for

replacing :

Now we substitute in the equation we had found for