JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Waves & Sound

The distance between two crests must be a whole number of wavelengths, $n\lambda =5$, and the distance between a crest and a trough must be an odd number of half-wavelengths, $(2m+1)\frac{\lambda }{2}=1.5$, with $n$ and $m$ integers. From the first, $\lambda =\frac{5}{n}$; substituting into the second gives $(2m+1)\frac{5}{2n}=1.5$, i.e. $5(2m+1)=3n$. The integer solutions $(m=1,n=5),(m=4,n=15),(m=7,n=25),\dots$ give $\lambda =1,\frac{1}{3},\frac{1}{5},\dots$, so the possible wavelengths are $1,\frac{1}{3},\frac{1}{5},\dots$ m.