Question

If ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$ are wavelengths of the waves giving resonance with fundamental, first and second over tones of a closed organ pipe, the ratio of wavelengths ${\lambda }_1$ : ${\lambda }_2$ : ${\lambda }_3$ is

• A. $1:2:3$
• B. $1:5:7$
• C. $1:3:5$
• D. $5:3:1$

Answer 1

The correct option is C $1:3:5$

For close ended pipe, frequency $=(2n-1)v/4(L+D)$
where n = integer; v = Speed of sound; L = length of the tube D = diameter of the tube.
Now frequency $=v/\lambda$
(2n -1)
Putting values of n as $1,2,3$ we get:

$1:2:3=1:(2+1):(4+1)=1:3:5$