What formula do I have to use?

Sorry, we don’t do your homework for you.

But if you take a stab at the answer, you might get a helpful response.

Your question does not state if the string is sharp or flat compared to what it is supposed to be.

This answer may be slightly off key:

All you need is a pitch pipe with A above middle C and you can loosen or tighten the string to match.

@ChipSkylark3220 The clue I will give you is Mersenne’s Laws. Like the others said, we don’t do people’s homework for you. But that should point you in the right direction.

@zenvelo We don’t need to know whether the note is sharp or flat to solve the problem, not least because this is a math/physics question and not a question about the actual practice of piano tuning. The relevant equation includes four variables and can be solved for any one of them given the other three.

@SavoirFaire But you need to know whether to tighten or loosen the string. And one does not ever need to know what the tension is to tune the piano.

The question might as well be “what tune can be played on the cables of the Golden Gate Bridge?”

@zenvelo But again: it’s a word problem, not a practical question. The bit about the note being slightly off is not relevant to what is actually being tested. A more direct version of the question would be something like, “what is the tension of a string with a linear mass density of 2 g/m and a length of 65 cm when tuned to 440 Hz?” There is a known formula for determining this that has nothing to do with the actual mechanics of tuning a piano, and the question is a way of checking whether someone can apply that formula correctly. It’s no different than checking if a first grader knows that 5 – 3 = 2 by asking “if Sandy has five apples and she gives three away, how many does she have left?”