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
$l=\frac{\lambda _{p}}{4}, \, \lambda =4l, \, n_{p}=\frac{v}{\lambda _{p}}=\frac{v}{4 l}$
$l=\frac{\lambda _{q}}{2},\lambda _{q}=2l, \, n_{q}=\frac{v}{\lambda _{q}}=\frac{v}{2 l}$
$l=\lambda _{r}, \, \lambda _{r}=l, \, n_{r}=\frac{v}{\lambda _{r}}=\frac{v}{l}$
$l=\frac{3 \lambda _{s}}{4}, \, \lambda _{s}=\frac{4 l}{3}, \, n_{s}=\frac{v}{\lambda _{s}}=\frac{3 v}{4 l}$
$\therefore n_{p}:n_{q}:n_{r}:n_{s}=\frac{v}{4 l}:\frac{v}{2 l}:\frac{v}{l}:\frac{3 v}{4 l}=1:2:4:3$