Two vibrating tuning forks produce progressive waves given by $Y_1 = 4\sin(500\pi t)$ and $Y_2 = 2\sin(506\pi t)$. The number of beats produced per minute is:

$41$ tuning forks are arranged in increasing order of frequency. Each tuning fork produces $5 \, \text{beats/sec}$ with the next one. If the frequency of the last tuning fork is double that of the first, what are the frequencies of the first and last tuning forks?

When two tuning forks are sounded together,$6$ beats per second are heard. One of the forks is in unison with $0.70 \ m$ length of a sonometer wire and another fork is in unison with $0.69 \ m$ length of the same sonometer wire. The frequencies of the two tuning forks are:

Two tuning forks $A$ and $B$ produce notes of frequencies $258 \,Hz$ and $262 \,Hz$. An unknown note sounded with $A$ produces certain beats. When the same note is sounded with $B$, the beat frequency gets doubled. The unknown frequency is (in $\,Hz$)

When a tuning fork of frequency $341 \ Hz$ is sounded with another tuning fork,six beats per second are heard. When the second tuning fork is loaded with wax and sounded with the first tuning fork,the number of beats is two per second. The natural frequency of the second tuning fork is: (in $Hz$)

The frequencies of tuning forks $A$ and $B$ are respectively $3\%$ more and $2\%$ less than the frequency of tuning fork $C$. When $A$ and $B$ are simultaneously excited,$5$ beats per second are produced. Then the frequency of the tuning fork $A$ (in $Hz$) is