A vibrating string of certain length 'l' under a tension 'T' resonates with a mode corresponding to the first overtone of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats/s, when vibrated along with a tuning fork of frequency 'n' . Increasing the tension of the string reduces the beat frequency. The frequency 'n' of the tuning fork in Hz is Velocity of sound in air is 3

Step-by-step solution

The frequency of the first overtone for an air column inside a tube closed at one end corresponds to the third harmonic, which is given by: f = 3v 4L Substituting v = 340 m/s and L = 75 cm = 0.75 m : f = 3 340 4 0.75 = 340 Hz Since the vibrating string resonates with this mode, the initial frequency of the string is f_s = 340 Hz . The string produces 4 beats/s with a tuning fork of frequency n . Thus, the possible frequencies of the tuning fork are: n = f_s 4 n = 340 + 4 = 344 Hz or n = 340 - 4 = 336 Hz The frequen