Q 11-14-107JEE MainJEE Main 2020 (4 Sep, Shift 1)Medium
For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5\ \text{m}$, while the distance between one crest and one trough is $1.5\ \text{m}$. The possible wavelengths (in m) of the waves are:
Answer: (B) $\dfrac11, \dfrac13, \dfrac15, \ldots$
Crest to crest: $5 = n\lambda$. Crest to trough: $1.5 = \left(m + \tfrac12\right)\lambda = \dfrac{(2m+1)\lambda}{2}$, so $\lambda = \dfrac3{2m+1}$.
Both hold if $\dfrac5n = \dfrac3{2m+1}$, i.e. $\lambda = 1$ (n = 5), $\tfrac13$ (n = 15), $\tfrac15$ (n = 25), ... so $\lambda = \dfrac11, \dfrac13, \dfrac15, \ldots$
Solution by Sreeraj P, M.Sc Physics