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,
$l=\frac{{\lambda }_p}{4},{\lambda }_p=4l,n_p=\frac{v}{{\lambda }_p}=\frac{v}{4l}$
$l=\frac{{\lambda }_q}{2},{\lambda }_q=2l,n_q=\frac{v}{{\lambda }_q}=\frac{v}{2l}$
$l=\lambda r,{\lambda }_r=1,n_r=\frac{v}{{\lambda }_r}=\frac{v}{l}$
$l=\frac{3{\lambda }_s}{4},{\lambda }_s=\frac{4l}{3},n_s=\frac{v}{{\lambda }_s}=\frac{3v}{4l}$
$l=\frac{3\lambda s}{4},{\lambda }_s=\frac{4l}{3}$
$h_s=\frac{v}{{\lambda }_s}=\frac{3v}{4l}$
$\therefore n_p:n_q:n_r:n_s=\frac{v}{4l}:\frac{v}{2l}:\frac{v}{l}:\frac{3v}{4l}=1:2:4:3$