Answer
50 Hz, and the 6th overtone.
Work Step by Step
We are told to model the alpenhorn as an open tube. The fundamental frequency is $f=\frac{v}{2\mathcal{l}}$.
$$f=\frac{343m/s}{2(3.4m)}\approx 50\;Hz$$
The overtones are whole multiples of the fundamental frequency.
$$f_n=nf_1$$
According to table 12-3, the note $F^{\#}$ is 370 Hz. Find the number of the harmonic.
$$n=\frac{f_n}{f_1}=\frac{370Hz}{50Hz}=7.4$$
The 7th harmonic, or the 6th overtone, is the note that is closest to $F^{\#}$.
