Question

A closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio

• A. \(3:4\)
• B. \(2:3\)
• C. \(4:5\)
• D. \(1:2\)

Hint:

Remember: Closed pipe supports only odd harmonics, open pipe supports all harmonics.

Answer 1

The Correct Option is A

Step 1: First overtone frequencies.
For closed organ pipe, first overtone corresponds to 3rd harmonic: \[ f_c = \frac{3v}{4L_c} \]
For open organ pipe, first overtone corresponds to 2nd harmonic: \[ f_o = \frac{v}{L_o} \]

Step 2: Equate frequencies.
\[ \frac{3v}{4L_c} = \frac{v}{L_o} \]

Step 3: Find ratio of lengths.
\[ \frac{L_c}{L_o} = \frac{3}{4} \]