MHTCET 5 May 2025 Shift 2 Paper

Concept:A closed organ pipe produces only odd harmonics, and overtones are the harmonics above the fundamental.Explanation:Fundamental frequency is $f_1 = 1500\ \mathrm{Hz}$.The normal hearing limit is $19500\ \mathrm{Hz}$.For a closed pipe, allowed frequencies are $f = (2n-1)f_1$, where $n = 1, 2, 3, \ldots$Set the highest audible frequency: $(2n-1) \times 1500 \le 19500$.This gives $2n-1 \le \frac{19500}{1500} = 13$, so $2n \le 14$ and $n \le 7$.Thus the audible harmonics are: $1500, 4500, 7500, 10500, 13500, 16500, 19500\ \mathrm{Hz}$.These are the 1st, 3rd, 5th, 7th, 9th, 11th and 13th harmonics.Only the fundamental is not an overtone.So the number of overtones = total harmonics − fundamental = $7 - 1 = 6$.Answer:The maximum number of overtones audible is $6$, which is Option A.