Question about Inverse Square law and sound intensity

[Hannes]

Homework Statement

For school, I have to make a task about sound intensity and the distance to the sound source. I have to prove that the relation between these two is known as the inverse square law _1/ I_2 = ( _2/_1 )².
Does someone know how I can plot the inverse square law or prove that it counts for this graph?
Thanks

Homework Equations

The Attempt at a Solution

 

[haruspex]

Does someone know how I can plot the inverse square law

A good approach is plot a function of the data which ought to yield a straight line. So if you expect y=1/x² then plot x² on one axis and 1/y on the other; or 1/x² on one and y on the other, etc.
Does that help?

 

[Hannes]

Yes that should normally be the plot of the inverse square law but in this case I have 0.0000002/x^1,975 and not 1/x^1.975 and I don't know how to solve that.

 

[haruspex]

Yes that should normally be the plot of the inverse square law but in this case I have 0.0000002/x^1,975 and not 1/x^1.975 and I don't know how to solve that.

Experimental data will never perfectly fit the theoretical curve. Indeed, it is not possible to prove physical theories, it is only possible to disprove them or to fail to disprove them (which is called confirming them).
So here you just need to show that the data are consistent an inverse square law, within the bounds of experimental error.

Another way to plot the data as a straight line is on a log-log graph.

 

[Hannes]

But this fits far from perfectly and we can't find our mistake.

 

[haruspex]

But this fits far from perfectly and we can't find our mistake.

Oh, I thought you were worried about the 1.975, instead of 2.
The constant multiplier can be anything. 0.0000002 is as good as any.