A glass rod, whose length is $l=110 \mathrm{~cm}$, was reinforced at its center, horizontally aligned, and a paraffin wax wick was attached to one of its ends. If we polish this rod with a wet paraffin wax candle, it will enter a longitudinal vibration, whose node is at the center. The frequency of the resulting sound was determined as follows. A Kundt's tube was attached to the end of the paraffin wax wick, which contained paraffin powder. The air in the tube resonated with the longitudinal vibrations of the glass rod, and the powder gathered in nodes at intervals of $l^{\prime}=12 \mathrm{~cm}$. The speed of sound in air is $V=340 \frac{\mathrm{m}}{\mathrm{sec}}$. What is the frequency of the resulting sound? What is the speed of longitudinal waves in the glass?
Let the wavelength of the generated sound in air be: $\lambda$, in glass: $\lambda^{\prime}$; then $\lambda=2 l^{\prime}$, because the nodes are half a wavelength apart, and $\lambda^{\prime}=2 l$, because if the node is in the middle, then from the middle to the end (the point of maximum vibration) a quarter wavelength is formed. But

$$
\lambda=\frac{V}{N}
$$

and thus

$$
N=\frac{V}{2 l^{\prime}}
$$

similarly

$$
\lambda^{\prime}=\frac{V}{N}
$$

and thus

$$
V^{\prime}=N 2 l=V \frac{l}{l^{\prime}}=3007 \frac{\mathrm{m}}{\sec }
$$

(Henrik Fodor, Beregszász.)