Question

A closed pipe is $25cm$ long. The velocity of sound in air is$330m{s^{ - 1}}$. How do you calculate the frequency of the fundamental vibration mode?

Answer 1

Hint : In a closed pipe, one end is opened and the other one is closed. Whenever there is an antinode at the open side and a node at the closed end, it forms a standing wave. There will be one node and one antinode which form the lowest frequency standing wave pattern. Thus, the wavelength is $4L$ for a pipe of length$L$. Frequency is defined as the speed of sound per unit wavelength. Hence the formula use is $f = \dfrac{v}{{4L}}$.

Complete Step By Step Answer:
The formula used for calculating the fundamental frequency of closed pipe of length $L$ and when the speed of light is $v$ :
$f = \dfrac{v}{{4L}}$
Substituting the values we will get,
v = 330m{s^{ - 1}} \\\ L = 0.25m \\\ f = \dfrac{{330}}{{4 \times 0.25}} \\\ f = \dfrac{{300}}{1} \\\ f = 300Hz \\\
Hence, the frequency is 300Hz.

Note :
Fundamental wave is the longest standing wave in a closed pipe. The next longest wave is the third harmonic. Organ pipe produces an antinode at the open side and a node at the closed end, only if it’s a closed organ pipe. If it’s an open organ pipe then nodes are produced in the middle of the pipe and antinodes are created at the ends.