Question

An air column, closed at one end and open at the other end, resonates with a tuning fork of frequency n when its lengths are 45 cm, 99 cm and at two other lengths in between these values. The wavelength of sound in the air column is

• A. 180 cm
• B. 108 cm
• C. 54 cm
• D. 36 cm

Answer 1

The correct option is D 36 cm

Initial frequency, $f_1=\frac{nv}{4l}$

Final frequency, $f_2=\frac{(n+3)v}{4l}$

$f_2-f_1=\frac{3V}{4l}=54cm$

But $\frac{V}{2l}=\lambda$ $\Rightarrow \frac{3\lambda }{2}=54cm$

$\Rightarrow \lambda =36cm$