Waves

JEE Main level, single correct, medium

38 of 142

Question 38 of 142

For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is 5m5\text{m}, while the distance between one crest and one trough is 1.5m1.5\text{m}. The possible wavelengths (in m\text{m}) of the waves are:

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Answer: (B) 11,13,15,.....\dfrac{1}{1},\dfrac{1}{3},\dfrac{1}{5},.....

Trough to crest distance
1.5=(2n1+1)λ21.5=\left(2{n}_{1}+1\right)\dfrac{\lambda }{2} ......(1)(1)
Trough to trough distance
5=(n2λ)5=\left({n}_{2}\lambda \right) .....(2)(2)
from (1)(1) and (2)(2)
1.55=2n1+12(n2)\dfrac{1.5}{5}=\dfrac{2{n}_{1}+1}{2\left({n}_{2}\right)}
3n2=10n1+53{n}_{2}=10{n}_{1}+5
n1{n}_{1} and n2{n}_{2} are integer
(1)(1) n1=1,n2=5,λ=1{n}_{1}=1, {n}_{2}=5, \lambda =1
(2)(2) n1=4,n2=15,λ=1/3{n}_{1}=4, {n}_{2}=15, \lambda =1/3
(3)(3) n1=7,n2=25,λ=1/5{n}_{1}=7, {n}_{2}=25, \lambda =1/5

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