I can't watch your video because I'm on dial-up and it takes forever to
download videos for me.
But, it sounds to me like either the rubber washer (if there is one) in
the water shut off valve to the machine is loose and vibrating, or one
of the rubber diaphragms in the water mixing valve is vibrating. I'm
thinking that if the noise made by the water mixing valve inside the
washer is bouncing off the wall behind the washer, it could sound like
it's coming from the water shut-off valves.
Two things to note:
1. The way to pinpoint the source of noises in machinery (like a washing
machine) is with an inexpensive tool called a "mechanic's stethoscope",
which will cost between $10 and $15 at any place that sells tools:
You just wear them on your head, and the noise you hear through the
"headphones" will be loudest when you're touching the metal probe to the
part that's actually making the noise.
2. Washing machines use something called a "mixing valve" to allow hot
water, cold water, or both to flow into the machine during the wash and
rinse cycles. The way these mixing valves work is that they actually
use the water pressure itself to stop the flow into the washing machine.
It's a very reliable system, but it can be screwed up by dirt in the
water, like rust and sand.
What I would do is:
a. While the machine is filling on a WARM WASH setting, close the hot
and cold water supply valves to the washer individually to see whether
the hot or cold side is making the noise. If the noise changes or stops
when you close the cold water supply valve, then it's the cold water
side that's making the noise. Ditto for the hot side.
b. Shut the water off to your house or laundry room, and take the
cartridge out of the water shut off valve on the side that's making the
noise (if it has a cartride). Confirm that the screw that holds the
rubber washer is in tight.
c. Take the hose to the washing machine off on the side that's making
noise and check the screen washer in the end of the hose to ensure it's
not clogged up with crap. The screens will either be brass or stainless
steel and you can buy replacement screened hose washers at any hardware
store or appliance parts store.
d. If you still come up empty, then I would buy a mechanic's
stethoscope and check the mixing valve in the washer to see if the whine
is coming from there. If so, replace the mixing valve. (Some appliance
companies used to sell overhaul kits for their washer mixing valves, but
I don't think they're available anymore.) Expect to pay between $20 and
$30 for a new water mixing valve for your washer.