For formation of beats, two sound notes must have

A stretched string fixed at both ends has ' $m$ ' nodes, then the length of the string will be

A stretched wire of length 260 cm is set into vibrations. It is divided into three segments whose frequencies are in the ratio $2: 3: 4$. Their lengths must be

A simple harmonic progressive wave is represented as $y=0.03 \sin \pi(2 t-0.01 x) \mathrm{m}$. At a given instant of time, the phase difference between two particles 25 m apart is