Turning on one faucet will cause a pressure drop at any other faucet that is running, but you say it is a "significant" drop - that implies that you have low water pressure, period. You might to consult with a plumber to see if anything can be done - if you live in a house with very old steel Plumbing pipes, replacing them can make a noteworthy difference (it's not cheap, of course).
Or possibly, you have an unusually low pressure system, perhaps a gravity feed system. Installing a water pump will solve any inconvenience, such as the shower almost quitting when a toilet is flushed elsewhere.
The faucet is clogged
A clogged aerator on the end of the faucet would cause the water flow to decrease in that faucet.
check for leaks
Possibly a pressure reducing valve installed after piping for first faucet, which would cause situation describing.
Unscrew the aerator from the end of the faucet where the water comes out and clean the screen. Sediment build up slows the flow.
A loose bolt or screw is the most common cause for a leaky faucet
It means that you should sell your home and move far away! No jk If its your faucet that is dripping I think in time your faucet needs repaired or replaced because if it drips only when you run water at another fixture (faucet) and doesn't drip if you have everything off then you have a strange faucet but its most likely caused by water hammer (sudden stop of water flow) and if you don't think its cause by that then it also could be from water pressure which when you turn on another faucet and the pressure drops a little and from the drop of pressure and it vibrates your seal in your faucet which could make it drip but very rare but possible.
You have a high iron content in your water. There are systems to correct this but there not cheap.
Kinked hose or obstruction in the water line between the wall and the faucet.
excessive velocity
Nothing, it can not do that .
A Pegasus faucet may be a good place to put in bathroom or kitchen sinks. This faucet is a great home decoration cause it has such an elegant look to it.