We know that the wavelength and frequency determine the speed of a wave. They are related by the following formula:

$$
begin{equation}
v = lambda cdot f
end{equation}
$$

We know that for the first harmonic only half a wavelength fits on a string. Therefore the wavelength is:

$$
begin{align*}
lambda = 2L = 2 cdot 1.3text{ m} = 2.6text{ m}
end{align*}
$$

Since we now know the wavelength, and we know the speed to be equal $v = 22 ; frac{text{m}}{text{s}}$, the frequency of the wave can be determined using the formula (1) as follows:

$$
begin{align*}
v &= lambda cdot f \
f_1 &= frac{v}{lambda}
end{align*}
$$

Plugging in the numbers we get:

$$
begin{align*}
f_1 = frac{22 ; frac{text{m}}{text{s}}}{2.6text{ m}} approx 8.5text{ Hz}
end{align*}
$$

We know that the wavelength and frequency determine the speed of a wave. They are related by the following formula:

$$
begin{equation}
v = lambda cdot f
end{equation}
$$

For each harmonic the wavelength depends only on the length of the string, which is kept constant.

Since the wavelength is constant looking at formula (1) easily gives that to increase the frequency $f$ we need to increase the speed of the wave in the string, since:

$$
begin{align*}
f sim v
end{align*}
$$