$A$ 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 .... $\text{Hz}$

$A$ 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 ... $Hz$.

$A$ string under a tension of $129.6 \ N$ produces $10 \ beats/s$ when it is vibrated along with a tuning fork. When the tension in the string is increased to $160 \ N$,it sounds in unison with the same tuning fork. Calculate the fundamental frequency of the tuning fork in $Hz$.

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 waves of wavelengths $99\, cm$ and $100\, cm$ both travelling with velocity $396\, m/s$ are made to interfere. The number of beats produced by them per second is

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 $......... \, Hz$.