Two vibrating strings $A$ and $B$ produce beats of frequency $8 \ Hz$. The beat frequency is found to reduce to $4 \ Hz$ if the tension in the string $A$ is slightly reduced. If the original frequency of $A$ is $320 \ Hz$, then the frequency of $B$ is: (in $Hz$)

Two tuning forks $X$ and $Y$ have frequencies $280 \,Hz$ and $284 \,Hz$. $A$ third tuning fork $Z$ has an unknown frequency. When $X$ and $Z$ are sounded together, a certain number of beats per second are heard. When $Y$ and $Z$ are sounded together, the beat frequency is found to be three times as great. The frequency of $Z$ is: (in $\,Hz$)

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 $Y_1 = 0.25 \sin(316t)$ and $Y_2 = 0.25 \sin(310t)$ are propagating along the same direction. The number of beats produced per second is:

$A$ tuning fork gives $3$ beats with $50 \ cm$ length of sonometer wire. If the length of the wire is shortened by $1 \ cm$,the number of beats is still the same. The frequency of the fork is (in $Hz$)

There are three sources of sound of equal intensity with frequencies $400, 401$ and $402\, vib/sec.$ The number of beats heard per second is