Two tuning forks $A$ and $B$ produce $4$ beats per second. The frequency of $A$ is $256 \ Hz$. On loading $B$ slightly,the beat frequency becomes $5$ beats in $2$ seconds. The frequency of $B$ after loading is .... $Hz$

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 $\,Hz$)

When two tuning forks (fork $1$ and fork $2$) are sounded together,$4$ beats per second are heard. Now some tape is attached to the prong of fork $2$. When the tuning forks are sounded again,$6$ beats per second are heard. If the frequency of fork $1$ is $200 \,Hz$,then the original frequency of fork $2$ is ........... $Hz$.

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 tuning forks $P$ and $Q$ are vibrated together. The number of beats produced are represented by the straight line $OA$ in the following graph. After loading $Q$ with wax,they are vibrated together again and the beats produced are represented by the line $OB$. If the frequency of $P$ is $341 \ Hz$,the frequency of $Q$ will be ... $Hz$.

$A$ 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 ..... $m$.