A tuning fork and an air column whose temperature is $51^{\circ} C$ produce $4$ beats in one second, when sounded together. When the temperature of air column decreases the number of beats per second decreases. When the temperature remains $16^{\circ} C$ only one beat per second is produced. The frequency of the tuning fork is ........... $Hz$
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(d)
$\frac{F+4}{F+1}=\sqrt{\frac{273+51}{273+16}}$
$\frac{f+4}{f+1}=\sqrt{\frac{324}{289}}$
$\frac{f+4}{f+1}=\frac{18}{17}$
$f=50 \,Hz$
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