$A$ tuning fork of unknown frequency produces $4$ beats per second when sounded with another tuning fork of frequency $254 \,Hz$. It gives the same number of beats per second when the unknown tuning fork is loaded with wax. The unknown frequency before loading with wax is ..........

An unknown frequency $x$ produces $8$ beats per second with a frequency of $250 \ Hz$ and $12$ beats per second with a $270 \ Hz$ source. Then $x$ is .... $Hz$.

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

$A$ tuning fork of known frequency $256\,Hz$ produces $5$ 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

Draw graphs of beats produced by two harmonic waves of frequency $11 \ Hz$ and $9 \ Hz$.

Two identical straight wires are stretched so as to produce $6$ beats per second when vibrating simultaneously. On changing the tension in one of them,the beat frequency remains unchanged. Denoting by ${T_1}$ and ${T_2}$ the higher and the lower initial tensions in the strings,respectively,then it could be said that while making the above change in tension: