If\[{{\lambda }_{1}},\,\,{{\lambda }_{2}}\]and\[{{\lambda }_{3}}\]are the wavelengths of the waves giving resonance with the fundamental, first and second overtones respectively of a closed organ pipe. Then the ratio of wavelengths\[{{\lambda }_{1}}:{{\lambda }_{2}}:{{\lambda }_{3}}\]
A)\[1:3:5\]
B)\[1:2:3\]
C)\[5:3:1\]
D)\[1:\frac{1}{3}:\frac{1}{5}\]
Correct Answer:
D
Solution :
According to the question \[\Rightarrow \] \[{{\lambda }_{1}}=2l\] \[l=\frac{3{{\lambda }_{2}}}{2}\Rightarrow {{\lambda }_{2}}=\frac{2l}{3}\] \[l=\frac{5{{\lambda }_{3}}}{2}\Rightarrow {{\lambda }_{3}}=\frac{2l}{5}\] \[\therefore \] \[{{\lambda }_{1}}:{{\lambda }_{2}}:{{\lambda }_{3}}=2l:\frac{2l}{3}:\frac{2l}{5}\] \[=1:\frac{1}{3}:\frac{1}{5}\]