Beats are produced by two waves $y_1 = a \sin(1000 \pi t)$ and $y_2 = a \sin(998 \pi t)$. The number of beats heard per second is

Two strings $X$ and $Y$ of a sitar produce a beat frequency of $4 \ Hz$. When the tension of the string $Y$ is slightly increased,the beat frequency is found to be $2 \ Hz$. If the frequency of $X$ is $300 \ Hz$,then the original frequency of $Y$ was .... $Hz$.

Two tuning forks of frequencies $320 \,Hz$ and $480 \,Hz$ are sounded together to produce sound waves. The velocity of sound in air is $320 \,ms^{-1}$. The difference between the wavelengths of these waves is nearly: (in $cm$)

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 $\,Hz$)

$A$ tuning fork of known frequency $256\,Hz$ produces $5$ beats per second with the vibrating string of a guitar. The beat frequency decreases to $2$ beats per second when the tension in the guitar string is slightly increased. The frequency of the guitar string before increasing the tension was ..... $Hz$.

The velocity of sound in a gas,in which two wavelengths $4.08\,m$ and $4.16\,m$ produce $40$ beats in $12\,s$,will be ..............$m\,s^{-1}$.