ExamBro
ExamBro
MHT CET · Physics · Waves and Sound

If ' \(l\) ' is the length of the open pipe, ' \(r\) ' is the internal radius of the pipe and ' \(V\) ' is the velocity of sound in air then fundamental frequency of open pipe is

  1. A \(\frac{\mathrm{V}}{(l+0.3 \mathrm{r})}\)
  2. B \(\frac{\mathrm{V}}{(l+1.2 \mathrm{r})}\)
  3. C \(\frac{\mathrm{V}}{(l+0.6 \mathrm{r})}\)
  4. D \(\frac{\mathrm{V}}{2(l+1.2 \mathrm{r})}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\mathrm{V}}{2(l+1.2 \mathrm{r})}\)

Step-by-step Solution

Detailed explanation

For an open organ pipe, the length of the pipe with end correction is given as:
\(
\begin{aligned}
& \mathrm{L}=l+2 \mathrm{e}=l+2 \times 0.6 \mathrm{r} \\
& \mathrm{L}=l+1.2 \mathrm{r}
\end{aligned}
\)
\(\therefore \quad\) The fundamental frequency of open pipe is:
\(
\begin{aligned}
& \mathrm{f}=\frac{\mathrm{v}}{2 \mathrm{~L}} \\
& \mathrm{f}=\frac{\mathrm{v}}{2(l+1.2 \mathrm{r})}
\end{aligned}
\)