# For a transverse wave travelling along a straight line, the distance between two peaks

Question:

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 :

1. $1,2,3$,

2. $\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \ldots$

3. $1,3,5, \ldots \ldots$

4. $\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots$

Correct Option: , 4

Solution:

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 $\mathrm{C}=\mathrm{n}_{2} \lambda$

$\frac{1.5}{5}=\frac{\left(2 n_{1}+1\right)}{2 n_{2}} \Rightarrow 3 n_{2}=10 n_{1}+5$

$\mathrm{n}_{1}=1, \mathrm{n}_{2}=5 \rightarrow \lambda=1$

$\mathrm{n}_{1}=4, \mathrm{n}_{2}=15 \rightarrow \lambda=1 / 3$

$\mathrm{n}_{1}=7, \mathrm{n}_{2}=25 \rightarrow \lambda=1 / 5$