Скачать или смотреть How Loud Can You Play Your Music And Not Bother Your Neighbors (Sound Attenuation)

I used to play my music loud... now I spend an afternoon calculating and making a video about how to just barely not make your neighbors mad.

Link to useful online calculator https://www.omnicalculator.com/physic...

In this problem we want to find out how loud you can play music without bother your neighbors. We will be assuming open air and no wind.
The sound system is 5 ft away from the listener and 100 ft from the neighbor outside. These values are also listed in meters.
According to this website about 50 decibels is alound after 11 pm which is about the same sound level as traffic or a quiet conversation. We will set our neighbors threshold for calling the police at 50 decibels
So how do we go about solving this one?
First we need to get everything out of decibels so a decibel is Equal to the log of intensity of the neighbor hears over the threshold of hearing which is 10 to the negative 12 watts per meters squared
Next we can divide both sides by 10 to get into the units of bells
The way this bel works is that every time we increase the exponent by 1 more than the threashold of hearing we get 1 additional bell of loudness. So the formula is 12 which is the absolute value to the negative 12 it is raised to minus x which is plugged into the top of the fraction behind the negative sign of the power.
Solving this equation we get that the intensity at the neighbors location or numerator must be 10 to the negative 7 watts per meters squared
Now we need to recall the inverse square law which was covered in a previous video. The to long didn’t watch version is that the if a sound wave travels from the single source at a distance of radius 1 it is the intensity is broadcasted over 1 square
and at a distance of 2 radius 1s it is broadcasted over 4 square
and at distance of 3 radius 1’s it is broadcasted over 3 squared . the intensity traveling outwards is broadcasted over the inverse square of the number of initial radiuses it is from the source point. Intensity over radius squared
Doing some rearranging we get that the intensity at the listening condition which is radius 1 condition is equal to the intensity at the neighbors location divided by radius of listener divided by the radius of the neighbor squared.
Now we can plug in our neighbors intensity and the radius of listener and the radius of the neighbor
Pressing the enter key on our calculator we get 4 times 10 to the -5 watts per meters squared for the intensity at the listeners position from the speaker
Now we can plug this value into the decibel formula and we get a decibel reading of 76.02 decibels
So if 5 feet from the speaker it is 76.02 decibels which is about as loud as a vacuum cleaner at 100 ft it would be as loud as a quiet conversation. There will be a link to an online calculator you can use to check your work in the description below.
For kicks I decided to graph both the intensity in wats per meter squared and in decibels allowed at a distance of 5 ft. You can see here that the decibel scale is logarithmic and the watts per meter squared is a power function.
Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.