If `lambda_(1), lamda_(2)and lamda_(3)` are the wavelengths of the wave giving resonance with the fundamental, first and second overtones respectively of a closed orga pipe Then the ratio of wavelength `lambda_(1), lamda_(2)and lamda_(3)` is

Options

A. `1:3:5`
B. `1:2:3`
C. `5:3:1`
D. `1:(1)/(3):(1)/(5)`

Answer

D

Explanation

`1=(lambda_(1))/(2)` so `lambda_(1)=21`, Similarly
`1=(3lambda_(2))/(2)implieslambda_(2)=(21)/(3)`, `1=(5lambda_(3))/(2)implieslambda_(3)=(21)/(5)`
`:.lambda_(1) : lambda_(2) : lambda_(3)=21 : (21)/(3) : (21)/(3)=1: (1)/(3) : (1)/(5)`