Distance between trough and crest of a waves is 1.5 m while distance between two troughs is 5m. which of the following wavelength is possible.
1/2, 1/4, 1/6....
1,2,3...
1/1, 1/3, 1/6...
1,3,5....
Answers
it has given that distance between crest and trough of a wave is 1.5 m while distance between two trough is 5m.
we have to check, which of the following possible value of wavelength ?
- 1/2 , 1/4 , 1/6 ..
- 1, 2 , 3 ...
- 1/1 , 1/3, 1/5 ...
- 1, 3, 5...
solution : we know, wavelength is the minimum distance between two consecutive crest or two consecutive trough.
so, distance between crest to trough = (2n₁ + 1)λ/2 where n₁ is whole number.
similarly, distance between trough to trough = n₂λ
where n₂ is whole number.
but given, 1.5 = (2n₁ + 1)λ/2 ......(1)
and 5 = n₂λ......(2)
dividing equation (1) by (2) we get,
1.5/5 = (2n₁ + 1)/2n₂
⇒3n₂ = 10n₁ + 5
if n₁ = 1 , n₂ = 5 ⇒ λ = 1
if n₁ = 4, n₂ = 15 ⇒λ = 1/3
if n₁ = 7, n₂ = 25 ⇒λ = 1/5
.... .. ... . .... ... ...
so, possible wavelengths are 1, 1/3, 1/5 .... i.e., correct option is (3) 1, 1/3, 1/5 ...