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
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
- A
$344$
- B
$336$
- C
$117.3$
- D
$109.3$
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- [AIPMT 1993]
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