Apiano tuner stretches a steel piano wire with a tension of 1000 n. the wire is 0.5 m long and has a mass of 5 g. what is the number of the highest harmonic that could be recorded by a computer that is capable of sensing frequencies up to 10,000 hz

The frequencies of the n-harmonics of a string is given by

where n is the number of the harmonic, L the length of the wire, T the tension and  is the linear density, with m being the mass of the string.
Let's calculate the linear density first, using the mass :

The problem says that the computer is able to analyze frequencies up to 10000 Hz. This means that we have to find the highest number of harmonic that generates a frequency smaller than this value. So, using , the tension of the string  and the mass m and the length of the string L, we can re-arrange the previous formula to find which n corresponds to this frequency:

And since n can only be integer, the highest harmonic that can be analyzed by the computer is n=31.