# Question about Inverse Square law and sound intensity

• Hannes
In summary, the conversation discusses how to plot and prove the inverse square law for sound intensity and distance to the sound source. The suggested approach is to plot a function of the data to yield a straight line, and to show consistency within experimental error. Another method is to use a log-log graph. The conversation also notes that experimental data may not perfectly fit the theoretical curve.
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

## The Attempt at a Solution

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.

## What is the inverse square law?

The inverse square law states that the intensity of a wave is inversely proportional to the square of the distance from its source. This means that as the distance from the source increases, the intensity of the wave decreases.

## How does the inverse square law apply to sound intensity?

The inverse square law also applies to sound intensity, meaning that as the distance from a sound source increases, the intensity of the sound decreases. This is why sounds become quieter the further away you are from their source.

## What are the units of sound intensity?

Sound intensity is measured in decibels (dB), which is a logarithmic unit that represents the ratio of the sound's intensity to a reference intensity. The reference intensity is usually set at the threshold of human hearing, which is 0 dB.

## How does sound intensity affect our perception of loudness?

The perceived loudness of a sound is not directly related to its intensity. Instead, our perception of loudness is affected by a combination of factors, including the sound's frequency, duration, and even our own individual hearing abilities.

## Can the inverse square law be applied to all types of waves?

Yes, the inverse square law can be applied to all types of waves, including light, sound, and electromagnetic waves. This is because the intensity of a wave decreases as it spreads out over a larger area, following the same principle of the inverse square law.

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