Inverse Square Law HELP PLEASE

[RichardGib]

Homework Statement

If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels?

&

If I measure a sound pressure of 1.0 at distance R from its source, what pressure would I measure at distance 2R in a free, unbounded space? What is the difference in decibels?

Homework Equations

N/A

The Attempt at a Solution

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I am stuck on this. i thought the answer to the first question could be a difference of -18db? Really stuck here...

Thankyou!

 

[Fightfish]

The inverse square law simply means that the value of the physical observable involved is inversely proportional to the square of the distance from the source. That is to say, for instance if the distance is doubled, then the value falls to a quarter (half squared).

 

[BvU]

Hello Richard, welcome to PF :)

Please check the PF guidelines (especially #4); the way you post now actually prevents us from helping you further.

And you can read up on the subject a little here

 

[RichardGib]

Hello Richard, welcome to PF :)

Please check the PF guidelines (especially #4); the way you post now actually prevents us from helping you further.

And you can read up on the subject a little here

Thankyou :)

 

[HalfLostAndSearching]

I am here to help you understand the concept of the Inverse Square Law. This law states that the intensity or power of a point source decreases in proportion to the square of the distance from the source. In other words, as you move further away from the source, the intensity decreases exponentially.

For your first question, if you measure a sound intensity of 1.0 at distance R, then at distance 3R, the intensity would be 1/9 or 0.111. The difference in decibels can be calculated using the formula 10 log (1/0.111) = 10 log 9 = 9 dB. This means that the sound intensity at 3R would be 9 decibels lower than at R.

For your second question, if you measure a sound pressure of 1.0 at distance R, then at distance 2R, the pressure would be 1/4 or 0.25. The difference in decibels can be calculated using the formula 20 log (1/0.25) = 20 log 4 = 6 dB. This means that the sound pressure at 2R would be 6 decibels lower than at R.

I hope this helps you understand the Inverse Square Law better. Remember, as distance increases, the intensity or pressure decreases, and the difference in decibels follows a logarithmic scale.