Standing Wave in String and Organ Pipe: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Standing Wave in String and Organ Pipe. Understanding the underlying formula is key to arriving at the correct answer below:

2nd overtone of open pipe = $3 \times (v / 2L_{\text{open}})$. 1st overtone of closed pipe = $3 \times (v / 4L)$. Equating them: $3v / 2L_{\text{open}} = 3v / 4L \Rightarrow L_{\text{open}} = 2L$.