$A$ 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 ..........

Beats are produced by two waves $y_1 = a \sin(1000 \pi t)$ and $y_2 = a \sin(998 \pi t)$. The number of beats heard per second is

$A$ wire vibrates at a fundamental frequency of $500 \,Hz$. $A$ second identical wire produces $5$ beats per second with it when the tension in the first wire is slightly decreased. The ratio of the tension in the second wire to the tension in the first wire is approximately equal to

Two waves of lengths $50 \; cm$ and $51 \; cm$ produce $12$ beats per second. The velocity of sound is .... $m/s$.

Two waves with amplitudes $3 \, m$ and $5 \, m$ produce beats. What is the ratio of the maximum to minimum intensity?

$A$ vibrating tuning fork of frequency $n$ is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through $8.75 \, cm$,the intensity of sound changes from a maximum to a minimum. If the speed of sound is $350 \, m/s$,then $n$ is .... $Hz$.