For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5 \mathrm{~m}$, while the distance between one crest and one trough is $1.5 \mathrm{~m}$. The possible wavelengths (in $\mathrm{m}$ ) of the waves are :
Correct Option: , 4
Given $\mathrm{T}$ to $\mathrm{C} 1.5 \mathrm{~m}$
$\mathrm{C}$ to $\mathrm{C} 5 \mathrm{~m}$
$\mathrm{T}$ to $\mathrm{C}=\left(2 \mathrm{n}_{1}+1\right) \frac{\lambda}{2}$
$\mathrm{C}$ to $\mathrm{C}=\mathrm{n}_{2} \lambda$
$\frac{1.5}{5}=\frac{\left(2 n_{1}+1\right)}{2 n_{2}} \Rightarrow 3 n_{2}=10 n_{1}+5$
$\mathrm{n}_{1}=1, \mathrm{n}_{2}=5 \rightarrow \lambda=1$
$\mathrm{n}_{1}=4, \mathrm{n}_{2}=15 \rightarrow \lambda=1 / 3$
$\mathrm{n}_{1}=7, \mathrm{n}_{2}=25 \rightarrow \lambda=1 / 5$
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