A vibrating string of certain length l under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased, the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is

Explanation

With increase in tension , frequency of vibrating string will increase. Since, number of beats are decreasing. Therefore , frequency of vibrating string or third harmonic frequency or closed pipe should be less than the frequency of tuning fork by `4` .
`:.` Frequency of tuning fork = third harmonic frequency of closed pipe `+ 4`
= `3 ((upsilon)/(4l)) + 4 = 3 ((340)/(4xx0.75)) + 4`
= `344 H_(Z)`
`:.` Correct option is (a).