Instead of changing the the frequency you can change the tension to produce the next higher harmonic. What percentage of the tension would produce the next higher harmonic?

Explanation:

This is a string resonance exercise, the wavelengths in a string held at the ends is

          λ = 2L₀ / n

where n is an integer

the speed of the wave is

           v = λ f

            f = v /λ

the speed of the wave is given by the characteristics of the medium (string)

           v =

we substitute  

            f =

to obtain the following harmonic we change n → n + 1

            f’ =  

In this case, it tells us to change the tension to obtain the same frequency.

            f ’= \frac{n}{2L_o} \  \sqrt{\frac{T}{\mu } }

how the two frequencies are equal

           (n + 1) = n

this is the relationship of the voltages to obtain the following harmonic,

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