Show that an wire tied at two end if it vibrates 1 loop, 2 loops, 3 loops & 4 loops., ratio of their frequency will be `1: 2: 3 : 4`.

The ratios of lengths, diameters and masses suspended from the free ends of two sonometer wires of the same meterial are 2 : 3 , 2 : 3 and 1 , 4 , respectively. What is the ratio of their fundamental frequencies ?

A stationary wave having 5 loops is generated in a 10 m long wire . What is the frequency, if the wave velocity is 20 m * s^(-1) ?

If the height of two right circular cylinder are in the ratio of 1:2 and perimeter of the bases are in ratio of 3:4, find the ratio of their volumes.

As shown in the figure. a wire is bent to form a 1 - shaped closed loop. carrying current I . where the curved part is a semi - circle of radius R . The loop is placed in a uniform magnetic field vec(B) . which is directed into the plane of the paper . The magnetic force felt by the closed loop is