Sound Dissipation: Find Equation to Measure How Far it Travels

[pmads]

I am not a physics student, although i have taken grade 11 physics :P, but i do have a general question to do with sound. My question came from this. There is suppose to be a rock concert about 4 Km away from my house. How many dbs would the concert have to produce in order for it to be barely audible (around 30 decibels) from my backyard at a tempterature of 25 degrees celcius (not sure if that matters for the distance sound can travel). So i guess what I am looking for is some sort of equation to measure how sound dissipates? Any help would be greatly appreciated, sorry if my question is lacking some key elements, let me know if you need more info.

 

[tiny-tim]

Welcome to PF!

There is suppose to be a rock concert about 4 Km away from my house. How many dbs would the concert have to produce in order for it to be barely audible (around 30 decibels) from my backyard at a tempterature of 25 degrees celcius (not sure if that matters for the distance sound can travel). So i guess what I am looking for is some sort of equation to measure how sound dissipates?

Hi pmads! Welcome to PF!

Assuming there's nothing in the way, it's an inverse-square law … the sound is 100 times quieter if it's 10 times further away … but some frequencies travel better than others (I don't know the reasons for that).

But remember two things …

i] houses and so on in the way will lessen the noise (so will mist)

ii] decibels are a "logarithmic" scale, not a linear one …

10 dB mean 10 times as loud, 20 dB means 100 times as loud …

so 10 times further away means 20 dB,

100 times further away means 40 dB …

 

[astrokreng]

Hello,

Thank you for reaching out with your question. I can provide some information on sound dissipation and how to measure it.

The equation to measure sound dissipation is called the Inverse Square Law. It states that the intensity of sound decreases by the square of the distance from the source. In other words, if you double the distance from the source, the sound intensity decreases by a factor of four. This applies to all sounds, including those from a rock concert.

To calculate the decibel level at a certain distance, you can use the following equation:

L1 = L2 + 20 log (d1/d2)

Where:

L1 = decibel level at distance d1

L2 = decibel level at distance d2

d1 = distance from the sound source

d2 = reference distance (usually 1 meter)

So, in your case, if the concert is 4 km away (4000 meters) and you want to know the decibel level at your backyard, you can use the equation as follows:

30 dB = L2 + 20 log (1/4000)

L2 = 30 dB - 20 log (1/4000)

L2 = 30 dB + 66.02

L2 = 96.02 dB

This means that the concert would have to produce at least 96.02 decibels for you to hear it at a distance of 4 km. Keep in mind that this is the theoretical decibel level, as other factors such as obstacles and wind can affect sound propagation.

I hope this helps. Let me know if you have any further questions. Good luck with your physics studies!