Q 11-14-017NEETJEE MainMedium
Two successive resonant frequencies of a pipe are $450$ Hz and $750$ Hz. The pipe is
Answer: (A) closed at one end, with fundamental $150$ Hz
Concept. An open pipe has all harmonics (spacing $f_1$); a closed pipe has only odd harmonics (spacing $2f_1$).
Step 1. Test an open pipe. $f_1 = 750 - 450 = 300$ Hz, but $450$ is not a multiple of $300$. ✗
Step 2. Test a closed pipe. $2f_1 = 300 \Rightarrow f_1 = 150$ Hz; then $450 = 3f_1$ and $750 = 5f_1$. ✓
Answer. Closed at one end, with fundamental $150$ Hz (Option A).
Solution by Sreeraj P, M.Sc Physics