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 vibrations. Find the length of the air columns. Neglect any end effect and assume that the speed of sound in air = 330 m/s.
Answer» Given that V = 330 m/s, the air columns in the U-tube are the closed organ pipes. The fundamental frequency V/4L = 440 Hz →L = V/(4440) m = 330/(4440) m →L = 3/16 m = 0.188 m = 18.8 cm The first overtone frequency is 3V/4L = 440 Hz →L = 3V/(4440) m =3330/(4440) m →L = 9/16 m = 0.563 m = 56.3 cm*

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 vibrations. Find the length of the air columns. Neglect any end effect and assume that the speed of sound in air = 330 m/s.

Answer»

Given that V = 330 m/s, the air columns in the U-tube are the closed organ pipes. The fundamental frequency

V/4L = 440 Hz

→L = V/(4*440) m = 330/(4*440) m

→L = 3/16 m = 0.188 m = 18.8 cm

The first overtone frequency is

3V/4L = 440 Hz

→L = 3V/(4*440) m =3*330/(4*440) m

→L = 9/16 m = 0.563 m = 56.3 cm

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