Two waves with amplitudes $3 \, m$ and $5 \, m$ produce beats. What is the ratio of the maximum to minimum intensity?

$A$ 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 $Hz$)

Two identical piano wires,kept under the same tension $T$,have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to the occurrence of $6\, beats/s$ when both the wires oscillate together would be:

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 .... $Hz$.

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 ........... $Hz$.

The frequencies of two tuning forks $A$ and $B$ are respectively $1.4 \%$ more and $2.6 \%$ less than that of the tuning fork $C$. When $A$ and $B$ are sounded together, $10$ beats are produced in $1 \text{ s}$. The frequency of tuning fork $C$ is: (in $\text{ Hz}$)