The white pipe is touching the copper pipe. The copper pipe is unsupported.

Open the diverter and grab the copper pipe going to the shower head with your hand. Does the noise stop?

Thanks for the reply!
I tried holding the copper pipe, but the noise doesn't fade nor change much. Also, when this noise/sound occurs, the water pressure drops significantly.

Again, the issue looks to be high pressure. Your water system would be better if you had a pressure arrester placed near the water meter. Depending on the time of day, water is less pressurized then others, as the water department adjust for the demand needed.
The fact that you have a humming noise still looks to be a issue with pipes vibrating due in part to not being secured properly. Possibly from the diverter to the shower head.

Good luck

Let's try two tests:

1) You hold the shower pipe while someone else opens the diverter.
2) Measure the water pressure: Water Pressure Gauge 0-160 - Heavy Duty - Mfg# 4106731
3) A water hammer arrester might help as well. "MINI-RESTER" WATER HAMMER ARRESTER 660-TR SIOUX CHIEF
Look at the mfr's website for more info.

On this page, you'll find stuff labeled ceiling flange and split pipe supports. These use 3/8 rod and a few nuts to lock the threaded rod to support pipes. This is how you can support the pipe going to the shower head. I do believe HD and Lowe's carry them.

For the water pressure gauge, I would need to place it between the diverter and the pipe leading to the shower head? I'll need to do some research to find out how (what materials I need) to cut & resolder the pipe.

No, you want to look at the house pressure. Should be about 55 PSI. The easiest place to temporarily connect is to a hose bib at a laundry sink, or outside faucet and even the drain of the water heater. I thought you would recognize that in the link. You can check house pressure anywhere.

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Originally Posted by fasthorse

Now if I flush the toilet, then the noise stops and the water pressure immediately increases. I should say that initially the water pressure is lower than normal.

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I'm looking at your above statement again. When you flush the toilet, the amount of cold water will decrease, so the amount of hot has to decrease to maintain the same temperature if the valve is temperature regulating. If it's not temperature regulating, then you should get a larger flow of warm water when the toilet is flushed.

Give me an idea of the relative position of the temperature setting as you are taking your shower. Do you have to fiddle with it during your shower? Is it near the hot position nearly all the time? Can you throttle back the cold supply to the shower? Do you know the model number of the mixing valve? Is a URL handy for an online version of the instructions?

I'm attacking from another angle.

The handle moves from -90 to about 80 degrees. I put the handle on 10 degrees so that it mixes hot and cold water.
When it makes that noise, I just move the handle below 0 degrees, then the noise immediately goes away since no hot water comes out then.
The entire shower kit was purchased from Rona, a Canadian home improvement store.
By mixing valve, you mean the gold/bronze-coloured device where all the pipes go into? Or do you mean the handle? On the oval metal plate, it says Branze, which I assume is the brand.

Are those screwdriver looking things in image 055 valves? There seems to be no way to adjust or move.

Is there hot and cold supply stops somewhere for the shower?

Where do you define 0 degrees. Use a clock. Can I assume the 12 o'clock position.

The valve turning is just temperature, right?

Yes, those are valves in image 055 and I can adjust them by taking off the oval plate from inside the shower.
Those can be adjusted though I am dumbfounded as to why nothing happens. I tried turning them both in one extreme direction and then in the other, but noticed no change.

As for the degrees, 0 degrees would be 6 o'clock and 80 degrees would be 1 o'clock.

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The valve turning is just temperature, right?

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Are you referring to the main shower handle? Or?

Yep, the temperature valve.

I think you need to find out what's in/not in those valves. I hope there is another way to turn off water to the shower.

What do you think, hk?

This is so strange and been going on so long I would not exclude anything at this point, including the shower head. Remove the shower head, inspect and make sure everything is clear. Turn on water to shower and run for several minutes with the head removed.

Did you ever black flush the valve. I would also remove the cartridge and flush out the valve. If problem persist I don't think you have any choice but to back flush the valve. To me it sounds like a piece of solder in the valve that requires a certain volume and pressure to vibrate. Temperature may even have something to do with it. This vibration is probably amplified by the metal studs of the wall.

After that you will probably have to consider if there is something unique about the valve it self that causing the vibration.

I have the same situation with the hum in the water pipes, running the shower, and flushing the toilet. HOWEVER, my pipes hum every time the water is turned on. The hum is extremely loud. You can hear it humming while in the shower, over the sound of the water running. It hummed when my hall bathroom toilet flapper was leaking, so it would kick on to refill the tank and bring it up to level and hum. I replaced the flapper. But sometimes at night my ice maker will kick on and that will cause it to hum. Everyone that comes to my house for the first time and uses the bathroom asks me why my house is humming.

I have a relatively new house, 3 yrs old, with blue pex for the cold water coming in from the meter. The house has a 4 foot crawl space underneath so I have been under there, and the cold water line hums and vibrates right where the pressure valve is. I just NOW turned on the water, went under the house and started grabbing the water line in various places. I found if I squeeze the line right above the pressure valve all the humming stopped. I'm talking LOUD humming, it has about driven me crazy! I found that if I squeezed the line a few inches above the valve I really had to put a grip on it. If I squeezed it right at the connection it didn't take as much pressure. So I ended up getting a 2x2 piece of wood and putting it between my foundation block and the line. There is just enough room to squeeze it in without putting undue stress on the connection. I had to push it down to meet the white connector crimped onto the pex and brass connector that went to the valve. Voilà... NO MORE HUM. I came back in, turned the water off and thought I had it solved. But when I flushed the toilet, it hummed again. I am getting that valve and that connection replaced. I believe the water line needs some type of vent too. Has anyone heard of pex humming if improperly vented?

Water supply pipes are not vented. Either the pressure reducing valve is defective or has trash or debris in it. Some PRV's have a screens in them that can be removed and cleaned.

When you pressed the line you stopped the line from vibrating. That stopped the sound. That did not stop what ever is vibrating inside the valve from vibrating. Vibration will probably change with volume of water flow.

Sounds more like a defective valve than debris in valve.