Two tuning forks $A$ and $B$ produce notes of frequencies $258 \,Hz$ and $262 \,Hz$. An unknown note sounded with $A$ produces certain beats. When the same note is sounded with $B$, the beat frequency gets doubled. The unknown frequency is (in $\,Hz$)

Two waves of wavelength $2 \ m$ and $2.02 \ m$ respectively,moving with the same velocity,superimpose to produce $2$ beats per second. The velocity of the waves is $... \ m/s$.

The frequencies of two tuning forks $A$ and $B$ are respectively $1.4 \%$ more and $2.6 \%$ less than that of the tuning fork $C$. When $A$ and $B$ are sounded together, $10$ beats are produced in $1 \text{ s}$. The frequency of tuning fork $C$ is: (in $\text{ Hz}$)

Two tuning forks,$A$ and $B$,produce $4$ beats per second when sounded together. The frequency of $A$ is $320 \ Hz$. When some wax is added to $B$ and it is sounded with $A$,$4$ beats per second are again heard. The frequency of $B$ is .... $Hz$.

Two sitar strings $A$ and $B$ playing the note 'Dhai' are slightly out of tune and produce beats of frequency $5 \; Hz$. The tension of the string $B$ is slightly increased and the beat frequency is found to decrease to $3 \; Hz$. What is the original frequency of $B$ if the frequency of $A$ is $427 \; Hz$ (in $; Hz$)?

Two waves $y_1 = 0.35 \sin(316 t)$ and $y_2 = 0.35 \sin(310 t)$ are propagating along the same direction. The number of beats produced per second is: