fluid dynamics - Why does a stream of water behave like this when aimed against a spoon or into a glass?

I noticed while doing everything except the dishes that water behaves quite strange. These two things might be two different phenomenon, but the water acts in a similar way in both cases.

Spoon and water stream
The width of the water stream changes upstream from where I insert the spoon. Since the water molecules are moving towards the spoon at a fairly high speed it seems like no motion should be able to travel up the stream. Why does this happen?

Here's a video of me playing with a spoon in the kitchen sink: https://youtu.be/VQeXM4EDb-Q

Water stream into glass
I managed to get this to turn into a periodic thing using a water glass while also avoiding doing the dishes, half a year later. Once again, the stream widens, but it goes further, until it collapses into a small stream and repeats.

I'm holding the glass as steady as I could, and the frequency does not have anything to do with my hand movements. Also, the exact position of the stream into the glass doesn't matter that much. I played with this for longer than I want to admit.

Here's a video of me playing with a glass in the kitchen sink: https://youtu.be/NBdkOtIAn9Y

Why does motion in water seem to move upstream, and why did the oscillation happen?

Answer

What you are seeing is the result of pressure waves moving upstream against the flow of the water.

Pressure waves in a fluid move at the speed of sound (because sound is a pressure wave) and in water this is around 1.5 km/sec. So while the water itself is moving downwards the pressure change caused by hitting an obstacle can propagate upstream as long as the speed of the water flow is less than 1.5 km/sec. If you inserted a pressure gauge in the water where it leaves the tap you would see the pressure increase when you put the spoon in the stream of water. This increase in the pressure in effect inflates the column of water, and this gives the effect you're seeing in the video.

To actually calculate the effect and predict its magnitude would be a formidable problem because even simple problems in fluid dynamics can be computationally intractable. The usual tactic is to give up and reach for a finite element analysis program and a large computer. I mention this to give myself an excuse for not explaining why you get the pulsing effect in your second video. It too will be due to pressure waves travelling upstream, but exactly why you get the oscillation I don't know.