For a transverse wave travelling along a straight line, the dista… - Vidyadip

MCQ

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
$1,2,3, \ldots \ldots$
B
$\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \ldots$
C
$1,3,5, \ldots$
✓
$\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots$

✓

Answer

Correct option: D.

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

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 $C = n _{2} \lambda$

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

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

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

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

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