Q 11-14-041JEE MainJEE Main 2024 (6 Apr, Shift 2)Medium
Two open organ pipes of lengths $60\ \text{cm}$ and $90\ \text{cm}$ resonate at their $6^{\text{th}}$ and $5^{\text{th}}$ harmonics respectively. The difference of frequencies for the given modes is ______ Hz. (Velocity of sound in air $= 333\ \text{m/s}$)
Numerical value type. Enter your answer.
Answer: 740
For an open pipe $f_n = \dfrac{nv}{2L}$:
$$f_6 = \frac{6\times333}{2\times0.6} = 1665\ \text{Hz},\qquad f_5 = \frac{5\times333}{2\times0.9} = 925\ \text{Hz}$$
Difference $= 740\ \text{Hz}$.
Solution by Sreeraj P, M.Sc Physics