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

Short Solution (Best for NEET):

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:

For the fifth overtone of a closed pipe, \(f_c = 11 \left(\frac{v}{4L_c}\right)\). For the third overtone of an open pipe, \(f_o = 4 \left(\frac{v}{2L_o}\right)\). Equating \(f_c = f_o\) yields \(\frac{L_c}{L_o} = \frac{11}{8}\).