$A$ tuning fork produces $4$ beats per second when sounded with a sonometer wire of vibrating length $48 \ cm$. It also produces $4$ beats per second when the vibrating length is $50 \ cm$,keeping the tension in the wire the same. What is the frequency of the tuning fork in $Hz$?

$A$ tuning fork and a sonometer wire are sounded together and produce $4$ beats per second. When the length of the sonometer wire is $95 \ cm$ or $100 \ cm$,the frequency of the tuning fork is ..... $Hz$.

$A$ string vibrates with a frequency of $200 \ Hz$. When its length is doubled and tension is altered,it begins to vibrate with a frequency of $300 \ Hz$. The ratio of the new tension to the original tension is

$A$ string is stretched between two fixed points separated by $75\,cm$. It is observed to have resonant frequencies of $420\,Hz$ and $315\,Hz$. There are no other resonant frequencies between these two. Then,the lowest resonant frequency for this string is ..... $Hz$.

$A$ device used for investigating the vibration of a fixed string or wire is

In a sonometer wire,the tension is maintained by suspending a $50.7 \, kg$ mass from the free end of the wire. The suspended mass has a volume of $0.0075 \, m^3$. The fundamental frequency of the wire is $260 \, Hz$. If the suspended mass is completely submerged in water,the fundamental frequency will become .... $Hz$ (take $g = 10 \, ms^{-2}$)