$A$ wave has simple harmonic motion whose period is $4\; s$,while another wave which also possesses simple harmonic motion has its period $3\; s$. If both are combined,then the resultant wave will have the period equal to ....... $s$.

$A$ pair of tuning forks produces $2$ beats in a time interval of $0.4 \ s$. The beat frequency is .... $Hz$.

Two wires are in unison. If the tension in one of the wires is increased by $2\%$,$5$ beats are produced per second. The initial frequency of each wire is .... $Hz$.

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

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:

$56$ 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 ..... $Hz$.