 # For a transverse wave travelling along a straight line, `
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. $1,3,5, \ldots \ldots$

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

3. $1,2,3, \ldots \ldots$

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

Correct Option: , 2

Solution:

(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.