Question

When an open pipe is closed from one end then the third overtone of the closed pipe is higher in frequency by $150 \, Hz$ than the second overtone of an open pipe. The fundamental frequency of the open-end pipe will be

• A. $75Hz$
• B. $150 \, Hz$
• C. $225 \, Hz$
• D. $300 \, Hz$

Answer 1

Answer: (D)

Let $f_{0}=\frac{v_{0}}{2 L}$ be the fundamental frequency of the open pipe
$\therefore \, \, $ is second overtone is $3f_{0}=\frac{3 v_{0}}{2 L}$
Let $f=\frac{v_{0}}{4 L}$ be the fundamental frequency of close pipe.
And third overtone of the organ pipe closed at one end only is, $\left(f_{3}\right)_{c l o s e d} \, =\frac{7}{4} \, \frac{v_{0}}{L}$
As given $\frac{7 v_{0}}{4 L}-\frac{3 v_{0}}{2 L}=150$
$\left(\frac{7}{4} - \frac{6}{4}\right) \, \frac{v_{0}}{L}=150$
$\therefore \, \frac{v_{0}}{4 L}=150$
$\frac{v_{0}}{2 L \, }= 300 Hz$