MHTCET 17 Apr 2026 Shift 1 Paper

Concept:Stationary waves in stretched strings and air columns have specific harmonic patterns. The harmonics and overtones are related by the mode number $n$.Explanation:For a stretched string fixed at both ends, the allowed frequencies are given by:$$f_n = n \frac{v}{2L}, \quad n = 1, 2, 3, \dots$$Here, $n = 1$ gives the fundamental frequency, which is the first harmonic:$$f_1 = \frac{v}{2L}$$The first overtone is the next allowed frequency above the fundamental. For $n = 2$:$$f_2 = 2 \frac{v}{2L} = 2f_1$$This frequency is called the second harmonic. Therefore, the first overtone is the same as the second harmonic.Now check the other statements. Consecutive antinodes are separated by $\frac{\lambda}{2}$, not by $\lambda$. A pipe open at both ends produces both odd and even harmonics. A pipe closed at one end produces only odd harmonics. Hence, these statements are incorrect.Answer:The correct statement is Option D: In the case of a stretched string, when vibrated, the frequency of the first overtone is the same as the second harmonic.