Question

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

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

Answer 1

The correct option is B $\frac{1}{1},\frac{1}{3},\frac{1}{5},......$

Given, The distance between one crest and one trough $=1.5\text{m}$

$(2n_1+1)\frac{\lambda }{2}=\frac{3}{2}\dots \left(1\right)$

Distance between two crests $=5\text{m}$
$n_2\lambda =5\dots \left(2\right)$
Here, $n_1$ and $n_2$ must be integers.
Putting the value of $n_1$ and $n_2$ in (1) and (2) we get,

If $n_1=1,n_2=5\Rightarrow \lambda =1\text{m}$
$n_1=4,n_2=15\Rightarrow \lambda =\frac{1}{3}\text{m}$
$n_1=7,n_2=25\Rightarrow \lambda =\frac{1}{5}\text{m}$
Hence, possible wavelengths are as follows, $\frac{1}{1},\frac{1}{3},\frac{1}{5}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.