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 .... $Hz$

$A$ tuning fork $A$ produces $4$ beats/sec with another tuning fork $B$ of frequency $320 \text{ Hz}$. On filing the fork $A$,$4$ beats/sec are again heard. The frequency of fork $A$ after filing is .... $\text{Hz}$

Two sitar strings $A$ and $B$ playing the note $'Ga'$ are slightly out of tune and produce beats of frequency $6 \ Hz$. The tension in the string $A$ is slightly reduced and the beat frequency is found to reduce to $3 \ Hz$. If the original frequency of $A$ is $324 \ Hz$,what is the frequency of $B$ in $Hz$?

Two identical piano wires have a fundamental frequency of $600 \text{ Hz}$ when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of $6$ beats per second when both wires vibrate simultaneously?

When a guitar string is sounded with a $440\, Hz$ tuning fork,a beat frequency of $5\, Hz$ is heard. If the experiment is repeated with a tuning fork of $437\, Hz$,the beat frequency is $8\, Hz$. The string frequency $(Hz)$ is

Two strings $A$ and $B$ produce beats of frequency $\Delta f_1 > 0$. The tension in string $A$ is slightly increased and the beat frequency is found to be $\Delta f_2 > 0$. If the original frequency of $A$ is $f_0$ and $\Delta f_2 < \Delta f_1$, then the frequency of $B$ is