Are liberty nickels affected by silver prices?

No, because Liberty nickels don't contain any silver. Like nearly all US nickels, they're made of an alloy of 25% nickel and 75% copper.

The only American nickels that ever contained silver were special "war nickels" minted from late 1942 to 1945. War nickels were made of an alloy of 56% copper, 35% silver, and 9% manganese because nickel metal was needed for the war effort. They can be identified by a large mint mark letter (P, D, or S) over the dome of Monticello on the back.