For transverse wave travelling along a straight line, the distance between two peaks (crests) is 5m, while the distance between one crests and one trough is 1.5m. The possible wavelengths (in m) of the waves are:
Option: 1 1,3,5,............
Option: 2 (1/1),(1/3,(1/5),............
Option: 3 1,2,3,..........
Option: 4 (1/2),(1/4),(1/6),.......... 

Answers (1)

Given trough to crest distance=1.5 m

So \left(2 n_{1}+1\right) \frac{\lambda}{2}=1.5

and crest to crest distance= 5 m

So

n_2\lambda =5

S0

from these two pieces of information, we get

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

And since n_1 \ \ and \ n_2 are integers

So

\begin{array}{l} \mathrm{n}_{1}=1, \mathrm{n}_{2}=5 \rightarrow \lambda=1 \\ \mathrm{n}_{1}=4, \mathrm{n}_{2}=15 \rightarrow \lambda=1 / 3 \\ \mathrm{n}_{1}=7, \mathrm{n}_{2}=25 \rightarrow \lambda=1 / 5 \end{array}

 

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