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 $\,Hz$)

$A$ vibrating tuning fork of frequency $n$ is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through $8.75 \, cm$,the intensity of sound changes from a maximum to a minimum. If the speed of sound is $350 \, m/s$,then $n$ is .... $Hz$.

$A$ sound wave travels with a velocity of $300 \, m \, s^{-1}$ through a gas. $9$ beats are produced in $3 \, s$ when two waves pass through it simultaneously. If one of the waves has a wavelength of $2 \, m$, the wavelength of the other wave is ..... $m$.

If the ratio of intensities of two waves is $4:1$,then the ratio of their maximum and minimum intensities is:

Two tuning forks of frequencies $256$ and $258$ vibrations/sec are sounded together,then the time interval between consecutive maxima heard by the observer is ..... $sec$.

Two sitar strings $A$ and $B$ playing the note '$Ga$' are slightly out of tune and produce beats of frequency $6 \; Hz$. The tension in the string $A$ is slightly reduced and the beat frequency is found to reduce to $3 \; Hz$. If the original frequency of $A$ is $324 \; Hz$,what is the frequency (in $Hz$) of $B$?