$A$ prong of a vibrating tuning fork is in contact with the water surface. It produces concentric circular waves on the surface of the water. The distance between five consecutive crests is $0.8 \ m$ and the velocity of the wave on the water surface is $56 \ m/s$. The frequency of the tuning fork is: (in $Hz$)

$A$ source of unknown frequency gives $4\, \text{beats/s}$ when sounded with a source of known frequency $250\, \text{Hz}.$ The second harmonic of the source of unknown frequency gives $5\, \text{beats/s}$ when sounded with a source of frequency $513\, \text{Hz}.$ The unknown frequency is .... $\text{Hz}$

$A$ tuning fork $A$ of frequency $250 \,Hz$ and another tuning fork $B$ of frequency $x$ produce $5$ beats per second when vibrated together. If the fork $B$ is waxed and vibrated together with $A$, then $3$ beats per second are produced. Then $x=$ (in $\,Hz$)

$A$ set of $28$ tuning forks is arranged in an increasing order of frequencies. Each fork produces '$x$' beats per second with the preceding fork and the last fork is an octave of the first. If the frequency of the $12^{\text{th}}$ fork is $152 \text{ Hz}$,the value of '$x$' (number of beats per second) is:

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 $\beta - \alpha$.

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