question_answer

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 \[\Rightarrow \]                               \[{{\lambda }_{1}}=2l\]                 \[l=\frac{3{{\lambda }_{2}}}{2}\Rightarrow {{\lambda }_{2}}=\frac{2l}{3}\]                 \[l=\frac{5{{\lambda }_{3}}}{2}\Rightarrow {{\lambda }_{3}}=\frac{2l}{5}\] \[\therefore \]  \[{{\lambda }_{1}}:{{\lambda }_{2}}:{{\lambda }_{3}}=2l:\frac{2l}{3}:\frac{2l}{5}\]                 \[=1:\frac{1}{3}:\frac{1}{5}\]