Two identical wires are vibrating in unison. If the tension in one of the wires is increased by $2 \%$,five beats are produced per second by the two vibrating wires. The initial frequency of each wire is $(\sqrt{1.02} \approx 1.01)$. (in $Hz$)

$P$ and $Q$ are two wires whose fundamental frequencies are $256 \ Hz$ and $382 \ Hz$ respectively. How many beats per second will be heard if the third harmonic of $P$ and the second harmonic of $Q$ are sounded together?

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

Two tuning forks $A$ and $B$ produce notes of frequencies $258 \,Hz$ and $262 \,Hz$. An unknown note sounded with $A$ produces certain beats. When the same note is sounded with $B$, the beat frequency gets doubled. The unknown frequency is (in $\,Hz$)

Two sitar strings $A$ and $B$ playing the note '$Ga$' are slightly out of tune and produce beats of frequency $6 \; Hz$. The tension in the string $A$ is slightly reduced and the beat frequency is found to reduce to $3 \; Hz$. If the original frequency of $A$ is $324 \; Hz$,what is the frequency (in $Hz$) of $B$?

Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t$. The number of beats produced per minute is