Question

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5\, m ,$ while the distance between one crest and one trough is $1.5\, m$. The possible wavelengths (in $m$ ) of the waves are

• A. $1,2,3, \ldots $
• B. $\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \ldots$
• C. $1,3,5, \ldots$
• D. $\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots$

Answer 1

Answer: (D)

Given $T$ to $C \,\,1.5 m$
$C$ to $C\,\, 5 m$
$T$ to $C =\left(2 n _{1}+1\right) \frac{\lambda}{2}$
$C$ to $C=n_{2} \lambda$
$\frac{1.5}{5}=\frac{\left(2 n _{1}+1\right)}{2 n _{2}} $
$\Rightarrow 3 n _{2}=10 n _{1}+5$
$n _{1}=1, n _{2}=5 \rightarrow \lambda=1$
$n _{1}=4, n _{2}=15 \rightarrow \lambda=1 / 3$
$n _{1}=7, n _{2}=25 \rightarrow \lambda=1 / 5$