Question

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

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

Answer 1

The correct option is D

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

Step 1 : Given data

Distance between two crests $=5m$

Distance between one crest and one trough $=1.5m$

$\lambda =$ Wave length

$n=$Number of waves

Step 2 : To find the wavelength

We know , distance between trough to crest $=\left(2n_1+1\right)\frac{\lambda }{2}$

Distance between crest to crest $=n_2\lambda$

$$\begin{gathered} \frac{1.5}{5}=\frac{\left(2n_1+1\right)}{2n_2} \\ 3n_2=10n_1+5 \end{gathered}$$

$$\begin{gathered} n_1=1,n_2=5,\to \lambda =1 \\ {n}_1=4,n_2=15\to \lambda =\frac{1}{3} \\ {n}_1=7,n_2=25\to \lambda =\frac{1}{5} \end{gathered}$$

Hence the possible wavelength of the waves are $\frac{1}{1},\frac{1}{3},\frac{1}{5}$

Therefore the correct answer is Option D