Tuning fork $F_1$ has a frequency of $256 Hz$ and it is observed to produce $6$ beats/second with another tuning fork $F_2$. When $F_2$ is loaded with wax,it still produces $6$ beats/second with $F_1$. The frequency of $F_2$ before loading was ..... $Hz$.

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?

It is possible to hear beats from two vibrating sources of frequency:

$A$ tuning fork of frequency $280\, Hz$ produces $10$ beats per second when sounded with a vibrating sonometer string. When the tension in the string increases slightly,it produces $11$ beats per second. The original frequency of the vibrating sonometer string is ... $Hz$.

In a guitar,two strings $A$ and $B$ made of the same material are slightly out of tune and produce beats of frequency $6 \, Hz$. When the tension in $B$ is slightly decreased,the beat frequency increases to $7 \, Hz$. If the frequency of $A$ is $530 \, Hz$,the original frequency of $B$ will be $......... \, Hz$.

$A$ tuning fork $A$ of unknown frequency produces $5 \, beats/s$ with a fork of known frequency $340 \, Hz$. When fork $A$ is filed,the beat frequency decreases to $2 \, beats/s$. What is the frequency of fork $A$ in $Hz$?