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: , 2
(2) Given : Distance between one crest and one trough
$=1.5 \mathrm{~m}$
$=\left(2 n_{1}+1\right) \frac{\lambda}{2}$
Distance between two crests $=5 \mathrm{~m}=n_{2} \lambda$
$\frac{1.5}{5}=\frac{\left(2 n_{1}+1\right)}{2 n_{2}} \Rightarrow 3 n_{2}=10 n_{1}+5$
Here $n_{1}$ and $n_{2}$ are integer.
If $n_{1}=1, n_{2}=5 \quad \therefore \lambda=1$
$n_{1}=4, n_{2}=15 \quad \therefore \lambda=1 / 3$
$n_{1}=7, n_{2}=25 \quad \therefore \lambda=1 / 5$
Hence possible wavelengths $\frac{1}{1}, \frac{1}{3}, \frac{1}{5}$ metre.