A particle of mass '$m$' is executing S.H.M. about the origin on x-axis with frequency $\sqrt{\dfrac{Ka}{\pi m}}$, where K is a constant and a is the amplitude of S.H.M. If '$x$' is the displacement of a particle at time '$t$', the potential energy of a particle will be

In an organ pipe closed at one end produces a fundamental note of frequency '$\nu$'. The pipe is cut into two pipes of equal length. The fundamental frequencies produced in the two pipes are

The fundamental frequency '$n$' of the tuning fork is 288 Hz, it will not resonate with the frequency

A wire of length 'L' and linear density 'm' is stretched between two rigid supports with tension 'T'. It is observed that wire resonates in the $P^{th}$ harmonic at a frequency of 320 Hz and resonates again at next higher frequency of 400 Hz in two successive modes. The value of 'P' is