Q 11-14-110JEE MainJEE Main 2019 (9 Jan, Shift 2)Medium
A musician using an open flute of length $50\ \text{cm}$ produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of $10\ \text{km h}^{-1}$. If the wave speed is $330\ \text{m s}^{-1}$, the frequency heard by the running person shall be close to
Answer: (C) $666\ \text{Hz}$
For an open pipe the $n$th harmonic is $f_n = \dfrac{nv}{2L}$:
$$f_2 = \frac{2\times330}{2\times0.5} = 660\ \text{Hz}$$
Observer speed $v_o = 10\times\dfrac{5}{18} = 2.78\ \text{m/s}$ towards the source:
$$f' = f\,\frac{v+v_o}{v} = 660\times\frac{332.78}{330} \approx 666\ \text{Hz}$$
Solution by Sreeraj P, M.Sc Physics