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