$A$ tuning fork sounded together with a tuning fork of frequency $256 \ Hz$ emits $2$ beats per second. On loading the tuning fork of frequency $256 \ Hz,$ the number of beats heard is $1$ per second. The frequency of the unknown tuning fork is: (in $Hz$)

When two tuning forks $A$ and $B$ are sounded together, $4$ beats per second are heard. The frequency of the fork $B$ is $384 \,Hz$. When one of the prongs of the fork $A$ is filed and sounded with $B$, the beat frequency increases. Then the frequency of the fork $A$ is: (in $\,Hz$)

In Melde's experiment in the transverse mode,the frequency of the tuning fork and the frequency of the waves in the strings are in the ratio

When two tuning forks are sounded together,$5$ beats per second are heard. One of the forks is in unison with $0.97 \ m$ length of sonometer wire and the other is in unison with $0.96 \ m$ length of the same wire. The frequencies of the two tuning forks are

The air columns in two tubes closed at one end vibrating in their fundamental modes produce $2$ beats per second. The number of beats produced per second when the same tubes are vibrated in their fundamental mode with their both ends open are

$56$ tuning forks are arranged such that each fork produces $4$ beats per second with its previous one. If the frequency of the last fork is twice that of the first, the frequency of the $19^{\text{th}}$ fork is . . . . . . (in $\text{Hz}$)