Wave Basics & Properties of Sound question from JEE Main 2020 (4 Sep, Shift 1)

Answer: (b)

1. Two crests are a whole number of wavelengths apart: $5 = n\lambda$.
2. A crest and a trough are an odd number of half wavelengths apart: $1.5 = (2m+1)\frac{\lambda}{2}$, so $\lambda = \frac{3}{2m+1}$.
3. Both hold for $\lambda = 1, \frac{1}{3}, \frac{1}{5}, \dots$ e.g. $\lambda = 1$: $5 = 5\lambda$, $1.5 = 3 \cdot \frac{\lambda}{2}$.
4. So the answer is (b) $\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \dots$