Question about Inverse Square law and sound intensity

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SUMMARY

The discussion centers on demonstrating the inverse square law in relation to sound intensity and distance from a sound source, specifically the equation _1/ I_2 = ( _2/_1 )². Participants suggest plotting the data in various ways, including using a log-log graph to visualize the relationship. They emphasize that experimental data may not perfectly align with theoretical predictions, highlighting the importance of consistency within experimental error rather than exact matches. The conversation also touches on the significance of constant multipliers in the equation, noting that variations like 0.0000002 are acceptable.

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  • Understanding of the inverse square law in physics
  • Familiarity with plotting functions and graphing techniques
  • Basic knowledge of logarithmic scales and log-log graphs
  • Concept of experimental error and data consistency
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  • Research methods for plotting inverse square law data using Python's Matplotlib
  • Explore the implications of experimental error in scientific data analysis
  • Learn about logarithmic transformations and their applications in data visualization
  • Investigate the significance of constant multipliers in physical equations
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Hannes
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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
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Homework Equations

The Attempt at a Solution

 
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Hannes said:
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?
 
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.
 
Hannes said:
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.
 
But this fits far from perfectly and we can't find our mistake.
 
Hannes said:
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.
 

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