The frequencies of two tuning forks $A$ and $B$ are $1.5 \%$ more and $2.5 \%$ less than that of the tuning fork $C$. When $A$ and $B$ are sounded together, $12$ beats are produced in $1$ second. The frequency of tuning fork $C$ is: (in $\text{ Hz}$)

The frequency of a tuning fork is $n \ Hz$ and the velocity of sound in air is $V \ m/s$. When the tuning fork completes $x$ vibrations,the distance traveled by the wave is:

The wavelengths of two notes in air are $\frac{36}{195} \,m$ and $\frac{36}{193} \,m$. Each note produces $10$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is

The wavelength of one wave is $99 \ cm$ and that of another is $100 \ cm$. If the speed of sound is $396 \ m/s$,the number of beats heard 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 $Hz$)

$A$ source of unknown frequency gives $4\, \text{beats/s}$ when sounded with a source of known frequency $250\, \text{Hz}.$ The second harmonic of the source of unknown frequency gives $5\, \text{beats/s}$ when sounded with a source of frequency $513\, \text{Hz}.$ The unknown frequency is .... $\text{Hz}$