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 = 330 m s-1.
Given:
Speed of sound in air 
Frequency of the tuning fork 
For the shorter arm:
Let the length of the shorter arm of the tube be 
.
Frequency of fundamental mode is given by:
On substituting the respective values, we get:
For the longer arm:
Let the length of the longer arm of the tube be 
.
Frequency of the first overtone 
Frequency of the first overtone is given by:
On substituting the respective values, we get:
