JEE PYQ: Waves And Sound Question 11
Question 11 - 2020 (04 Sep Shift 1)
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 :
(1) 1, 3, 5, …..
(2) $\frac{1}{1}, \frac{1}{3}, \frac{1}{5}$, ……
(3) 1, 2, 3, …..
(4) $\frac{1}{2}, \frac{1}{4}, \frac{1}{6}$, ……
Show Answer
Answer: (2)
Solution
Given: Distance between one crest and one trough $= 1.5$ m
$= (2n_1 + 1)\frac{\lambda}{2}$
Distance between two crests $= 5$ m $= n_2\lambda$.
$\frac{1.5}{5} = \frac{(2n_1 + 1)}{2n_2} \Rightarrow 3n_2 = 10n_1 + 5$
Here $n_1$ and $n_2$ are integer.
If $n_1 = 1, n_2 = 5$ $\therefore \lambda = 1$ $n_1 = 4, n_2 = 15$ $\therefore \lambda = 1/3$ $n_1 = 7, n_2 = 25$ $\therefore \lambda = 1/5$
Hence possible wavelengths $\frac{1}{1}, \frac{1}{3}, \frac{1}{5}$ metre.
BETA
