Question

In the fundamental mode, the time taken by the wave to reach the closed end of the air-filled pipe is $0.01s.$ The fundamental frequency is

• A. $25$
• B. $12.5$
• C. $20$
• D. $15$

Answer 1

The correct option is A

$25$

Step 1: Given

Time taken= $0.01s$

Time taken to reach the closed-end$=\frac{l}{v}=0.01s$

Step 2: Formula used

Frequency, $f=\frac{v}{\lambda }$,

Where,$f$= Frequency,$v$= velocity,$I$= Intensity and $\lambda$= Wavelength

$\begin{array}{rcl}\therefore f& =& \frac{l}{t\times \lambda }\\ & =& \frac{1}{(tx4l)}\left[\because v=\frac{{\displaystyle l}}{{\displaystyle t}}\right]\end{array}$

Step 3: Calculation
$\lambda =\frac{4l}{(2n-1)}$ where $l$ is the length of the closed organ pipe,

Assume n =1, then $\lambda =4l$

$\begin{array}{rcl}\therefore f& =& \frac{l}{t\times 4l}\\ & =& \frac{1}{(0.01x4)}\\ & =& 25\mathrm{Hz}\end{array}$

Hence, the correct option is (A).