Q 11-14-030JEE MainMedium
An open organ pipe has a fundamental frequency of $300$ Hz. The first overtone of a closed pipe has the same frequency as the first overtone of this open pipe. Find the length of the closed pipe, in cm. (speed of sound $= 330$ m/s)
Numerical value type. Enter your answer.
Answer: 41.25
Concept. Open pipe first overtone $= 2f_1$; closed pipe first overtone $= \dfrac{3v}{4L}$.
Step 1. Open pipe first overtone. $2 \times 300 = 600$ Hz.
Step 2. Closed pipe length.
$$\frac{3v}{4L} = 600 \;\Rightarrow\; L = \frac{3 \times 330}{4 \times 600} = 0.4125\ \text{m} = 41.25\ \text{cm}$$
Answer. $41.25$.
Solution by Sreeraj P, M.Sc Physics