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:

$A$ set of $24$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4 \, Hz$ beats per second with the preceding one and the frequency of the last tuning fork is two times that of the first fork,find the frequency of the $5^{th}$ tuning fork in $Hz$.

Two vibrating tuning forks produce progressive waves given by $y_1 = 4 \sin(500 \pi t)$ and $y_2 = 2 \sin(506 \pi t)$. These tuning forks are held near the ear of a person. The person will hear

An unknown frequency $x$ produces $8$ beats per second with a frequency of $250 \ Hz$ and $12$ beats per second with a $270 \ Hz$ source. Then $x$ is .... $Hz$.

Two waves of lengths $50 \; cm$ and $51 \; cm$ produce $12$ beats per second. The velocity of sound is .... $m/s$.

The frequency of a tuning fork is $256 \, Hz$. The velocity of sound in air is $344 \, ms^{-1}$. The distance travelled (in $meters$) by the sound during the time in which the tuning fork completes $32$ vibrations is