Sound intensity and distance problem

[foobarbazzer]

Homework Statement

Henry and Tom see a flash of lightning and then hear the resulting clap of thunder. Henry measures the sound level of the thunder as 65 dB while Tom, who is 800 m further from the event, measures it as 63 dB.

Homework Equations

The Attempt at a Solution

I_H / I_T = 1.58
1 / d^2 = 1/1.58
d = sqrt(1 / 1.58)
= 0.796
0.796 * 800 = 636 m away, yet the answer is 3090 m.

Why?

 

[PeterO]

Homework Statement

Henry and Tom see a flash of lightning and then hear the resulting clap of thunder. Henry measures the sound level of the thunder as 65 dB while Tom, who is 800 m further from the event, measures it as 63 dB.

Homework Equations

The Attempt at a Solution

I_H / I_T = 1.58
1 / d^2 = 1/1.58
d = sqrt(1 / 1.58)
= 0.796
0.796 * 800 = 636 m away, yet the answer is 3090 m.

Why?

In your calculation you say:

1 / d^2 = 1/1.58
d = sqrt(1 / 1.58)

Notice you have the reciprocal of the left [d] but not the reciprocal of the right.

You should have been taking the sqrt of 1,58.

Indeed you should not have rounded off, but been using 1.584893192 at least.

Once you have that answer consider the following.

If the answer had been 1.2, then 800m is the difference when going from 1 x distance from lightning to 1.2 x distance to lightning. 800m represents that extra 0.2, so the distance from Henry must have been 4000m
[ie 1.2 * 4000 = 4800 ; the extra 800m]

Now the answer is not 1.2, but that is how you have to treat the answer you do get.