An open organ pipe has its first overtone $N_{1}=512$, if it is blown with air (the speed of sound in air is $V=340 \frac{\mathrm{m}}{\mathrm{sec}}$). How high will the fundamental frequency of this pipe be if it is blown with hydrogen, in which the speed of sound is $V^{\prime}=1200 \overline{\mathrm{m}} \sec$?
For the first overtone, there are two nodes and the length of the string $(l)$ is equal to the wavelength $(\lambda)$

$$
l=\lambda=\frac{V}{N_{1}}
$$

For the fundamental tone, there is one node and the length of the string is equal to half the wavelength

$$
l=\frac{\lambda^{\prime}}{2}=\frac{V^{\prime}}{2 N_{0}}
$$

thus

$$
\frac{V}{N_{1}}=\frac{V^{\prime}}{2 N_{0}^{\prime}}
$$

from which

$$
N_{0}^{\prime}=\frac{V^{\prime}}{V} \cdot \frac{N_{1}}{2}=904
$$

(Kürth Richard, Nyitra.)

The problem was solved by: Ehrenstein P., Erdélyi I., Esztó P., Fekete M., Fodor H., Freund E., Heimlich P., Jánosy Gy., Szilas O., Sztrokay K.