$A$ 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 ... $Hz$.

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:

$56$ tuning forks are arranged in increasing order of frequencies in a series such that each fork gives $4 \text{ beats per second}$ with the previous one. The frequency of the last fork is the octave of the first. The frequency of the first fork is ..... $Hz$.

$A$ tuning fork of frequency $512\, Hz$ makes $4$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was .... $Hz$

$A$ tuning fork of frequency $100 \, Hz$ when sounded together with another tuning fork of unknown frequency produces $2$ beats per second. On loading the tuning fork whose frequency is not known and sounding it together with the tuning fork of frequency $100 \, Hz$,it produces one beat. The frequency of the other tuning fork is: (in $, Hz$)

What should be the frequency of beats so that they can be heard clearly in the case of sound?