Question

A column of some gas is open at one end and closed at the other. The shortest length of such a column that will resonate with a 350 Hz tuning fork is 28.0 cm. What is the speed of sound in this gas?

Answer 1

Answer:

392 m/s

Explanation:

In a closed pipe or column (one in which one end is open and the other is closed), resonance occurs at various lengths of the column depending on the frequency. The shortest column is formed when the frequency is the fundamental frequency.

At any frequency, the node of the standing wave is formed at the closed end while antinodes are formed at the open end. For the fundamental frquency, this standing wave is a quarter-wavelength long since this is the shortest distance between a node and antinode.

Thus, $l = \dfrac{\lambda}{4}$

$\lambda = 4l$

Now the speed of a wave is

$v=f\lambda$ where $f$ is its frequency

Hence, $v=f\times4l=4fl$

Substituting values in the question and converting cm to m,

$v=4\times 350\times 0.28 = 392 \text{ m/s}$