Question

In a long cylindrical tube the wave level is adjusted and the air column above it is made to vibrate in unison with a vibrating tuning fork kept at the open end. Maximum sound is heard when the air column lengths are equal to

• A. $\frac{\lambda }{4}$ , $\frac{3\lambda }{4}$
• B. $\frac{\lambda }{2}$ , $\frac{3\lambda }{2}$
• C. $\lambda ,3\lambda$
• D. $\lambda$ , $\frac{3\lambda }{4}$

Answer 1

The correct option is A $\frac{\lambda }{4}$ , $\frac{3\lambda }{4}$

So in general the formula for the resonance length will be:
$\frac{(2n-1)\lambda }{4}$, where $n=1,2,3$..
First booming sound indicates that at that length, $l_1$, of an air column in organ pipes with one end closed is in resonance with the given frequency.
And that length is,
$l_1=\lambda /4$
The next resonance length will be :
$l_2=3\lambda /4$