Question

If the velocity of sound in air is 336m/s. The maximum length of a closed pipe that would produce a just audible sound will be:
A. 3.2 cm
B. 4.2 m
C. 4.2 cm
D. 3.2 m

Answer 1

Maximum length of a closed pipe that would produce a just audible sound will be given as
$l=\dfrac{v}{4\nu }$
Where v is the velocity of sound in air, $\gamma$ is the lowest frequency which is audible. This equation can be useful in solving this question.

Complete step by step answer:
A closed pipe is the pipe in which one end is open and the other is closed. Like open pipes closed pipes can also form a standing wave with the waves of a sound of an appropriate frequency. There will be standing waves produced at higher frequencies which are higher than the fundamental frequency. These are generally called harmonics.
Now let us find the maximum length of a closed pipe that would produce a just audible sound,
As per the question, v is the velocity in air
V=336 m/s
The least frequency which can be audible by humans is 20 Hz.
Therefore as we all know,
The maximum length of a closed pipe that would produce a just audible sound will be given as

$l=\dfrac{v}{4\nu }$

Where v is the velocity of sound in air, $\gamma$ is the lowest frequency which is audible. That is 20 Hz.

$\begin{aligned} & l=\dfrac{336}{4\nu } \\\ & l=\dfrac{336}{4\times 20} \\\ & =4.2m \\\ \end{aligned}$

Therefore the maximum length of closed pipe that would produce audible sound=4.2m
So the correct answer is (B).

Note:
The lowest frequency which can be heard by humans is 20 Hz. A closed pipe is the pipe in which one end is open and the other is closed. Like open pipes closed pipes can also form a standing wave with the waves of a sound of an appropriate frequency.