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 ms^-1

A U-tube having unequal arm-lengths has water in it. A tuning fork of

1.	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 ms^-1
Answer» Solution :Let the length of the LONGER tube `L_2` and smaller will be `L_1`. According to the data `440=(3xx300)/(4L_2)`………1 (FIRST over TONE) and `440=(3xx330)/(4L_1)` ………..2 (Fundamental) SOLVING equation we get, `L_2=56.3cm` `and L_1=18.8cm`