waves Questions

A metal wire of linear mass density $9.8\text{g/m}$ is stretched with a tension of $10\text{kg-wt}$ between two rigid supports $1\text{metre}$ apart. The wire passes at its middle point between the poles of a magnet and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is:

A tuning fork of known frequency $256\text{Hz}$ makes $5$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:

The displacement $y$ of wave travelling in the $x$ -direction is given by $y=10^{-4}\sin (600t-2x+\pi /3)$ metres, where $x$ is in metres and $t$ in seconds. The speed of the wave-motion in $\text{m/s}$ is: