Question

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 ${\lambda }_1:{\lambda }_2:{\lambda }_3$ is

• A. 1 : 3 : 5
• B. 1 : 2 : 3
• C. 5 : 3 : 1
• D. 1 : $\frac{1}{3}$ : $\frac{1}{5}$

Answer 1

Answer: (D)

According to the question
$l=\frac{{\lambda }_1}{2}$
$\Rightarrow {\lambda }_1=2l$
$l=\frac{3{\lambda }_2}{2}\Rightarrow {\lambda }_2=\frac{2l}{3}$
$l=\frac{5{\lambda }_3}{2}\Rightarrow {\lambda }_3=\frac{2l}{5}$
$\therefore {\lambda }_1:{\lambda }_2:{\lambda }_3=2l:\frac{2l}{3}:\frac{2l}{5}$
$=1:\frac{1}{3}:\frac{1}{5}$