A steel rod $100\, cm$ long is damped at into middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\, kHz$. What is the speed of sound in sound is steel ? (in $km/s$)

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

If the tension of sonometer’s wire increases four times then the fundamental frequency of the wire will increase by …. $ times$

A string under a tension of $129.6\,\, N$ produces $10\,\, beats /sec$  when it is vibrated along with a tuning fork. When the tension is the string is increased to $160\,\, N,$ it sounds in unison with same tuning fork. calculate fundamental freq. of tuning fork …. $Hz$

The equation of a standing wave in a string fixed at both ends is given as $y=2 A \sin k x \cos \omega t$ The amplitude and frequency of a particle vibrating at the mid of an antinode and a node are respectively