The kids were playing in the oscillating/fan sprinkler in the yard and when I went inside it sounded very noisy in my basement. I discovered that the noise was coming from the copper pipes leading to the outside spigot. I went outside and opened the spigot fully (originally the valve was only partially open) and the noise from the pipes in my basement became much quieter. The spigot is an old standard hose bib style (not frost-free). I don't think it leaks when the valve is closed. It is attached to a 50 foot hose and there is a slight leak at that connection when the valve is open.

Is this most likely a bad pipe job? If so I can take a picture of the pipe pathway.

In the meantime I can use a different outside spigot that has a much shorter piping inside the house (and monitor the sound on that one to be safe).

If the leak is at the hose/spigot connection it is either a packing nut dripping down to the hose thread, or the connection from the hose to the spigot isn't great, usually an old washer in the hose isn't sealing well. Noise with high velocity water is common through hose bibbs due to turbulence as you have observed. Sometimes flipping the washer over in the hose can help if you don't have a replacement one handy, but enjoy watching the kids have fun and don't worry.