Discussion Forum

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

Answer:

Explanation:

According to question , fundamental

frequency of organ pipe is given by    $f_{0}=\frac{V_{0}}{2l}$

   [ Symbols have their usual meanings]

 In 2 nd overtone,   $\frac{3}{2}f_{0}=\frac{3V_{0}}{2l}$

 Let   $f=\frac{V_{0}}{4l}$ be the fundamental frequency of closed organ pipe. Third overtone of closed organ pipe at one end is

$f_{3}=\frac{7}{4}\frac{V_{0}}{l}$

 As given,    $\frac{7}{4}\frac{V_{0}}{l}-\frac{3 V_{0}}{2l}=150$

 $\Rightarrow$      $\left(\frac{7}{4}-\frac{6}{4}\right)\frac{V_{0}}{l}=150$

 $\Rightarrow$      $\frac{V_{0}}{4l}=150\Rightarrow \frac{V_{0}}{2l}=300 Hz$