Question

The vibrating of four air columns are represented in the figure. The ratio of frequencies $n_p:n_q:n_r:n_s$ is

• A. $12:6:3:5$
• B. $1:2:4:3$
• C. $4:2:3:1$
• D. $6:2:3:4$

Answer 1

Answer: (B)

As is clear from figure of question
$l=\frac{{\lambda }_p}{4},\lambda =4l,n_p=\frac{v}{{\lambda }_p}=\frac{v}{4l}$
$l=\frac{{\lambda }_q}{2},{\lambda }_q=2l,n_q=\frac{v}{{\lambda }_q}=\frac{v}{2l}$
$l={\lambda }_r,{\lambda }_r=l,n_r=\frac{v}{{\lambda }_r}=\frac{v}{l}$
$l=\frac{3{\lambda }_s}{4},{\lambda }_s=\frac{4l}{3},n_s=\frac{v}{{\lambda }_s}=\frac{3v}{4l}$
$\therefore n_p:n_q:n_r:n_s=\frac{v}{4l}:\frac{v}{2l}:\frac{v}{l}:\frac{3v}{4l}=1:2:4:3$