If two progressive sound waves represented by $y_1 = 3 \sin(250 \pi t)$ and $y_2 = 2 \sin(260 \pi t)$ (where displacement is in metre and time is in second) superimpose,then the time interval between two successive maximum intensities is (in $s$)

$A$ 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 ....... $s$.

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 identical piano wires,kept under the same tension $T$,have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to the occurrence of $6\, beats/s$ when both the wires oscillate together would be:

$A$ and $B$ are two wires whose fundamental frequencies are $256 \text{ Hz}$ and $382 \text{ Hz}$ respectively. When the third harmonic of $A$ and the second harmonic of $B$ are sounded together, the number of beats heard in two seconds will be:

Two vibrating tuning forks produce progressive waves given by ${y_1} = 4\,\sin \left( {500\pi t} \right)$ and ${y_2} = 2\,\sin \left( {506\pi t} \right)$. These tuning forks are held near the ear of a person. The person will hear $\alpha \, \text{beats/s}$ with intensity ratio between maxima and minima equal to $\beta$. Find the value of $\beta - \alpha$.