MHTCET 22 Apr 2025 Shift 1 Paper

Concept:An open pipe has fundamental frequency $f_o = \frac{v}{2L}$. A closed pipe of the same length has fundamental frequency $f_c = \frac{v}{4L}$, and it produces only odd harmonics.Explanation:Step 1: The pipe initially behaves as an open pipe, because its fundamental frequency is given as $80$ Hz.Step 2: When one end is closed, the pipe becomes a closed pipe of the same length $L$.Step 3: For the open pipe, $f_o = \frac{v}{2L} = 80$ Hz, hence $\frac{v}{L} = 160$ Hz.Step 4: For the closed pipe, fundamental frequency is $f_c = \frac{v}{4L} = \frac{160}{4} = 40$ Hz.Step 5: Closed pipes vibrate only at odd multiples of the fundamental: $f_n = (2n-1)f_c$, where $n = 1,2,3,\ldots$Step 6: Therefore, the allowed frequencies are $40, 120, 200, 280, \ldots$ Hz.This matches option C.Answer:Option C: $40, 120, 200, 280$ Hz.