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Please help me keep the lows in my own house

None of these are going to make any difference at low frequencies, especially LF TRANSMISSION through the walls, door and roof of what is an acoustically transparent garage.

there is a high difference between reflection and transmission, the DIFFERENCE is what’s responsible for the challenge the OP faces.
I stand 100% corrected!
For curiosity's sake, I ran the numbers to see what sort of diffuser it'd take to scatter 40Hz wavelengths effectively: you'd have projections up to ~4.3 meters long. So, for all intents and purposes, not space, weight, or cost effective. At all.
 
Firstly, kudos for trying to be the nice guy here and do the right thing.
It does sound like you've got an impossible ask here technically, and the best suggestions are those about trying to find a compromise with the neighbor(s).
I wouldn't bother with the DB meters and claiming by-law compliance. That only gives you the legal right, but you sound like you'd rather have folks on your side here.

One other thought I had was that maybe you could rent a rehearsal room someplace for the times you have to cut loose and play at full power.
Set up in your bedroom & sleep in your garage?

But seriously, I’d investigate whether some kind of tactile board would work.



...either in conjunction with headphones/in ears, or a split signal - sending the offending lows through the tactile board and the more controllable upper frequencies through your amp.

I’m just spitballing here.
 
Insulation will, in fact, absorb bass frequencies -- it just needs to be at least as thick as a quarter-wavelength of the frequency you want to absorb. For the approximately 40 Hz wavelength of a low E string, that's about 7 feet. Plus the sound source would still need to be contained in a more-or-less airtight room of sufficient mass and rigidity to avoid audible resonances and sympathetic vibration. There are a number of techniques to mitigate LF transmission, but none of them is cheap or easy. I hope that's evident to the OP by now.
 
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Several things come to mind immediately.

Question first. Did you just move in? If you've been there a while you already know who wrote the note. Or you can join the Nextdoor.com and you'll be able to see comments from one neighbor about the bass player next door and all the other neighbors commenting that they should let it go and find their own hobby. Other reason I asked, if you've been playing for a long time and they just suddenly decided to be jerks about it maybe look up the local noise ordinance and practice within that time line and push the limits. We're all musicians here, we all know a band in a house down the street isn't that hard to deal with. Just because you can hear it if you try does not make it a nuisance.

1) Classic flaming bag of dog poop at their front door. It's Halloween so wear a costume, even if they have a door camera you're in the clear.
2) Do donuts in their front yard. Also an oldie but goodie.
3) Have a block party and book your own band and invite everyone but them. Let them call the cops on the entire neighborhood.
4) Plant kudzu in their yard. And/or every time you find a dandelion collect it and toss on their grass.
5) Arrange service "quotes" for them. Every day. At 30 minutes before they leave for work and 30 minutes after they return. There are probably hundreds of window installers, roofers, tree trimmers, vinyl siding, carpet steamers, masons, landscapers, etc. Easily could last 3-4 weeks.
6) Volunteer! Start community Music Therapy for children in your community. No neighbor, no matter how mean, is ever going to complain about kids getting therapy and if they do complain, call the TV news local reporter and expose them.
7) Get to know them. Become friends. Go to their social club or sport or whatever, then create drama by spreading rumors or other creative initiative to turn their friends against them.
8) Follow them to work. Rent an RV. Then drive their commute in front of them every day for a week. When they confront you say "got nothing to do now that my band can't rehearse". Ask if they want to compromise.

Have fun with it.
 
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Not an easy or practical solution, but you could fill your wall spaces with sand. Short of that, bass waves tend to go right through ordinary construction materials. If you double or triple drywall your practice room, and build a second room within leaving an airspace between, this will help too.

The simple solution is to turn down or use headphones.
I didn't need to read any more of this thread after this first reply, he said it. best thing for you to do is build an isolation room inside your garage. That aint gonna happen for $500 though.

I'll say this though, whatever means you implement to help reduce sound wave and vibration transmission will have the added side effect of enabling you to actually BE quieter. You will not NEED to play as loudly ins aspace that is acoustically isolated and treated, since you will find you can hear everything ore clearly at lower volumes.
 
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I literally built a second interior wall, 2x6, fully insulated, plus using sound board, inside of the walls and ceiling that were already there. That meant additional work for the electric outlets as well. No one could hear anything after that, & I was playing loud with Marshall stacks.
 
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AgedHorse has the only answer. I started looking at doing this (room within a room with double sheetrock walls and ceiling) in my garage when I lived in a denser neighborhood. It was cheaper to move. Now my neighbors (coyotes squirrels and deer) rarely complain. Well, the coyotes get worked up a lot, but it seems unrelated to bass leakage.
 
Decent little reference document there.
Everything I mentioned earlier is contained in this document. Figure 10 (TRANSMISSION) shows WHY low frequency control is so difficult.

While the STC is represented as a single bandwidth limited number for noise control, in fact it’s a set of numbers and the lowest 2 octaves, the most difficult spectrum to control, are not even represented in the single number. It’s misleading unless you understand what the numbers mean and why they are chosen for architectural purposes.

Octave by octave calculations are used for STC when dealing with noise transmission in special use buildings like theatres, rehearsal spaces, recording studios and many large industrial facilities.

Acoustics is probably the most misunderstood subject on the internet, common sense without understanding the physics behind acoustics doesn’t appear to make any sense. The more you know about the physics behind acoustics, the better you can appreciate the challenges and complexity.

When designing speakers, understanding and properly applying all of these types of principles helps arrive at well performing designs without multiple trial and error attempts. Same applies to the OP’s problem, trial and error is a VERY expensive way to try solving a problem like this.
 
When law enforcement gets a complaint, no matter what time of day or night or what the noise ordinance says, they are obliged to respond and investigate. Sooner or later they are going to get tired of responding to the same complaint. Then they’re not going to be so nice.

I came within about ten seconds of getting these three sentences tattooed on my head with a nightstick back in 1986. Backyard high school party gig. I had RIGHTS! We had a noise ordinance! Said we were good until 10pm! Then just in time I remembered what my grandfather, retired ATF, said to me about "do whatever they tell you because I'm able to bail you out of jail but not out of the morgue", and it really was just in time because the sticks were out and those boys were ready to rock. So I told everyone to shut their pieholes and do whatever the nice boys in blue told us to do. They didn't break our gear, I'll say that for them. That happened to some friends of mine.

Turns out the real noise ordinance is whatever you most sensitive neighbor is willing to call the cops over. That's it.

OP, I got a rehearsal studio back then because we were loud as hell and there just wasn't any other way to make it work. Nowadays, I have a room inside the house (room in a bigger room) and at least twenty feet of separation from my closest neighbor. I run very low volume for bass and hot rods/pads on the drumkit, and only play drums when I know their kids are awake. I would not dare to have a band over for rehearsal. Low volume personal practice only. The problem with the instruments we play is that they carry through everything.

I know this is not on your list of options but you're simply going to have to turn down a lot. I despise headphones myself so I just play quietly. But the future for gigs (and I gig a lot when there is not a plague afoot) is in-ear on stage, so I'm thinking during this enforced downtime about trying a shaker board and my in-ears. Gonna have to get used to it. The guys running those systems around here have been the ones getting the lion's share of all the work.
 
I don’t think anything will work for $500 ... without changing your sound.

But you could try - Gaslighting your neighbour tell him/her your not playing music and it’s all in their head.

Stop playing when your neighbour is in.

Marry your neighbour.

——
Broughton HP filter is what I use.
 
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Have you tried it

I didn’t need to try it and waste a client’s money. The math showed that it is virtually 100% ineffective, we do the math because we are responsible professionals. “Guessing” is not a good defense when you get sued for an ineffective design.

Give your neighbors the $500 to put up with the noise.

This is not necessarily a bad idea in some instances.

Insulation will, in fact, absorb bass frequencies -- it just needs to be at least as thick as a quarter-wavelength of the frequency you want to absorb. For the approximately 40 Hz wavelength of a low E string, that's about 7 feet. Plus the sound source would still need to be contained in a more-or-less airtight room of sufficient mass and rigidity to avoid audible resonances and sympathetic vibration. There are a number of techniques to mitigate LF transmission, but none of them is cheap or easy. I hope that's evident to the OP by now.

7’ thick walls and ceilings make for either a tiny interior space or a giant structure;)

I literally built a second interior wall, 2x6, fully insulated, plus using sound board, inside of the walls and ceiling that were already there. That meant additional work for the electric outlets as well. No one could hear anything after that, & I was playing loud with Marshall stacks.

Electric guitar is much easier to control, for bass the issue is frequencies below 125Hz, which are harder to control.

SAFETY ALERT:
Also, something else to consider is that many common materials are NOT suitable for hanging on walls or ceiling as they have high vertical flame spread ratings. Just because carpet (for example) can be used on a floor (a horizontal surface) doesn’t mean that it’s suitable for a wall (vertical surface). Materials suitable for use in acoustical control will carry specific flame spread ratings for the intended surfaces. Why is this important? Look up the Station Nightclub fire and that’s why it’s not a good idea (and is in fact illegal in most jurisdictions)
 
7’ thick walls and ceilings make for either a tiny interior space or a giant structure;)
Yeah, expensive in space in addition to other costs. This is an inevitable problem in studio design -- dead air space is effective for isolation, but has a huge cost in real estate terms.

BTW, moving to the country hasn't been too effective around these parts; I know of at least one studio and one large outdoor venue that started out in relative isolation but were ultimately done in by the encroachment of 'civilization'. That studio worked successfully for years in what was essentially a glorified double-wide modular home, and even garnered a couple of Grammy's. The studio owner had several acres of property, but eventually the neighborhood grew up around him and started making it difficult to track after dark. In many cases, local sound ordinances are your friend, in that they define what the actual rules are -- when you can make sound, and how much. In the absence of an applicable noise ordinance, pretty much any complaint about excessive noise will result in a visit and admonishment from the local constabulary. Obviously, that doesn't figure in to this situation; nobody, but nobody should want to involve legal means in what is basically a neighborhood issue.
 
Sound proofing is a myth, you need sound absorption, and it will cost you way way way more than 500 dollars. Think pro studio type situation.

But I have a solution that fulfills your requirements. Use your 500 and pay a couple months rent at a lockout practice space, have your gear there and play as loud as you want and have band practices too.
 
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