Q 11-14-015NEETJEE MainMedium
A string fixed at both ends vibrates in its third harmonic at $300$ Hz. The string is $90$ cm long. The speed of waves on it is
Answer: (C) $180$ m/s
Concept. For the $n$th harmonic of a string fixed at both ends, $L = n\dfrac{\lambda}{2}$; then $v = f\lambda$.
Step 1. Wavelength. $0.9 = \dfrac{3\lambda}{2} \Rightarrow \lambda = 0.6$ m.
Step 2. Speed. $v = 300 \times 0.6 = 180$ m/s.
Answer. $180$ m/s (Option C).
Solution by Sreeraj P, M.Sc Physics