Question

The separation between a node and the next antinode in a vibrating air column is 25 cm. If the speed of sound in air is 340 m s⁻¹, find the frequency of vibration of the air column.

Answer 1

Given:
Separation between the node and anti-node = 25 cm
Speed of sound in air v = 340 ms⁻¹
Frequency of vibration of the air column f = ?
The distance between two nodes or anti-nodes is λ.
We have:
$$\begin{gathered} \frac{\lambda }{4}=25\mathrm{cm} \\ \Rightarrow \lambda =100\mathrm{cm}=1\mathrm{m} \end{gathered}$$
Also,
$v=f\lambda$
$\Rightarrow f=\frac{v}{\lambda }=\frac{340}{1}=340\mathrm{Hz}$
Hence, the frequency of vibration of the air column is 340 Hz.