When you pull down on the official app, there is a robotic chirp that sounds like a bird or Frog. Some people have been enamored with the sound while others don't like it.
Thankfully, there are a few ways to prevent you from hearing it.
My tests show that turning your phone to silent mode makes it so that the sound doesn't play. The ringer switch on the left side of the phone needs to be moved closer to the back of the phone in order for it to work.
The pull-to-refresh sound doesn't seem to have been rolled out to every phone. If you have it, you can usually silence your ringer through the menu that shows up after you use the volume buttons.
If you want your phone to make other noises, muting your phone isn't an ideal solution. The bad news is that the option to turn off the sound is not in the app.
If you want to access it, you have to go to the app and tap on your profile picture. Go to the settings and privacy for display and sound. Sound effects can be turned off.
There are different options and labels on the menu in the version of the app that's on the phone. You can turn off the sound effects in the app.
You should no longer hear the sound when you refresh a page after you turn off the toggle. I wasn't able to find any prominent ones that played when I had the toggle on, apart from the pull to refresh one.
Enjoy your quiet time.