Question

An organ pipe $\text{A}$ with both ends open, has a fundamental frequency of $300\text{Hz}$. The third harmonic of organ pipe $\text{B}$ with one end open, has the same frequency as the second harmonic of pipe $\text{A}$. What is the ratio of length of pipe $\text{A}$ to length of pipe $\text{B}$ ?

• A. $\frac{2}{5}$
• B. $\frac{3}{2}$
• C. $\frac{4}{3}$
• D. $\frac{3}{4}$

Answer 1

The correct option is C $\frac{4}{3}$

Given,
Fundamental frequency of open organ pipe $\text{A}$ is given by,
$f_{1A}=\frac{v}{2L_A}=300\text{Hz}$
Second harmonic of organ pipe $\text{A}$ is given by
$f_{2A}=\frac{2v}{2L_A}$ ($L_A=$ Length of pipe $\text{A}$)

Third harmonic of closed organ pipe pipe $\text{B}$ is given by
$f_{3B}=\frac{3v}{4L_B}$ ($L_B=$ Length of pipe $\text{B}$)

From the data given in the question,
$f_{2A}=f_{3B}$

$\Rightarrow \frac{2v}{2L_A}=\frac{3v}{4L_B}\Rightarrow \frac{L_A}{L_B}=\frac{4}{3}$

Hence, option (c) is correct