$A$ tuning fork of frequency $480 \ Hz$ produces $10$ beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces fewer beats per second than before?

The frequency of tuning fork $A$ is $256\,Hz$. It produces $4\,beats/sec$ with tuning fork $B$. When wax is applied to tuning fork $B$,$6\,beats/sec$ are heard. By reducing a small amount of wax,$4\,beats/sec$ are heard. The frequency of $B$ is .... $Hz$.

Two identical wires have a fundamental frequency $f_0$ when kept under the same tension $T$. If the tension of one wire is increased by $\Delta T$, then $N$ beats occur when both wires oscillate simultaneously. Find the expression for $\frac{\Delta T}{T}$.

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 $\,Hz$)

Two tuning forks $A$ and $B$ are sounded together and produce $6$ beats per second. The frequency of tuning fork $B$ is $384 \,Hz$. When tuning fork $A$ is loaded with wax,the number of beats per second becomes $4$. What is the frequency of tuning fork $A$ in $Hz$?

When an air column at $15 ^\circ C$ and a tuning fork are sounded together, $4$ beats per second are produced. The frequency of the fork is less than that of the air column. When the temperature falls to $10 ^\circ C$, the beat frequency decreases by one. The frequency of the fork will be ..... $Hz$ $[V_{sound}$ at $0 ^\circ C = 332, m/s]$.