Question

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

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

Answer 1

Answer: (B)

1 : 2 : 4 : 3

Find the figure,

In $p,L=\frac{{\lambda }_p}{4},$

$\therefore {\lambda }_p=4L$

$\Rightarrow n_p=\frac{V}{{\lambda }_p}=\frac{V}{4L}$

In $q,L=\frac{{\lambda }_q}{2},$

$\therefore {\lambda }_q=2L$

$\Rightarrow n_q=\frac{V}{{\lambda }_q}=\frac{V}{2L}$

In $r,L={\lambda }_r,$

$\therefore {\lambda }_r=L$

$\Rightarrow n_r=\frac{V}{{\lambda }_r}=\frac{V}{L}$

In $s,L=\frac{3{\lambda }_s}{4},$

$\therefore {\lambda }_s=\frac{4L}{3}$

Now, $n_p:n_q:n_r:n_s$

$=\frac{V}{4L}:\frac{V}{2L}:\frac{V}{L}:\frac{4L}{3}$

$=1:2:4:3$