$A$ 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?

Two identical stringed instruments have a frequency of $100 \ Hz$. If the tension in one of them is increased by $4\%$ and they are sounded together,then the number of beats produced in one second is:

$50$ tuning forks are arranged in increasing order of their frequencies such that each gives $4 \, \text{beats/sec}$ with its previous tuning fork. If the frequency of the last fork is the octave of the first, then the frequency of the first tuning fork is ... $Hz$.

Two identical straight wires are stretched so as to produce $6$ beats per second when vibrating simultaneously with tensions $T_1$ and $T_2$ respectively. On changing the tension slightly in one of them,the beat frequency remains unchanged. This will happen when (Given $\rightarrow T_1 > T_2$)

Two sound waves having displacements $x_1 = 2 \sin(1000 \pi t)$ and $x_2 = 3 \sin(1006 \pi t)$,when interfere,produce

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