Question

Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the range $(40-20000\text{Hz})$
[Assume, speed of sound in air = $340{\text{ms}}^{-1}$]

• A. $8.5\text{cm}$
• B. $4.25\text{cm}$
• C. $4.5\text{cm}$
• D. $2.25\text{cm}$

Answer 1

The correct option is B $4.25\text{cm}$

Modes of vibration of air column in an open organ pipe is given by
$f_n=\frac{nv}{2L}$

For maximum wavelength, the frequency is minimum.

Hence, $f_1=\frac{v}{2L}$

Given, minimum frequency is $f_1=40\text{Hz}$

From the data given in the question,
$40=\frac{340}{2L}$
$\Rightarrow L=\frac{340}{80}=4.25\text{cm}$

Thus, option (b) is the correct answer.