Question

A U-tube having unequal arm-lengths has water in it. A tuning fork of frequency 440 Hz can set up the air in the shorter arm in its fundamental mode of vibration and the same tuning fork can set up the air in the longer arm in its first overtone vibration. Find the length of the air columns. Neglect any end effect and assume that the speed of sound in air =$330m{s}^{-1}$.

Answer 1

Let the length of the longer tube be $"L_2"$ and smaller will be $L_1.$

According to the data

$440=\frac{3\times 300}{4L_2}.......\left(1\right)$

(First over tone)

and $440=\frac{3\times 330}{4L_1}.......\left(2\right)$

(Fundamental)

Solving equation we get,

$L_2=56.3cm$

and $L_1=18.8cm$