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

A

Explanation

As is clear from figure
`L=(lambda_(1))/(4)orlambda_(1)=4L,L=(3lambda_(2))/(4)orlambda_(2)=(4L)/(3)`
`L=(5lambda_(3))/(4)orlambda_(3)=(4L)/(5) therefore lambda_(1):lambda_(2):lambda_(3)=1:(1)/(3):(1)/(5)`