Magnetostriction:

When magnetic field is applied across the length of a ferromagnetic  rod such as Nickel, then change in the length of rod is observed. This is called Magnetostriction. The charge in length is propotional to the strength of megnetic field.  The increase in length is very small in practice. Amongst all ferromagnetic substances, increase in length is maximum for Nickel.

Production of ultrasonic waves:  

Experimental arrangement to produce Ultrasonic Waves by magnetostriction method is shown in figure. Here AB is a rod of nickel, which is clamped in the centre. Here T is a valve oscillator. On coil L₁ in the grid circuit of value oscillator is wound on one side of the rod and another L₂(also shown by thin line) in the anode circuit of valve is wound on the other side of the rod. The coil L₂ and variable capacitor C from a tank circuit, which produces electronic oscillations of frequency

                                                f = 1/ 2π√L₂C                          (1)

Due to this a longitudinal alteraning magnetic field is produced around the rod. The frequency of oscillation of magnetic field is also v as given in (1). Since capacitor C is variable capacitor. Hence by adjusting value of C, we can adjust the frequency of alternating magnetic field produced around the nickel rod. However the oscillations of magnetic field should be sustained(i.e. amplitude of magnetic field should not chand=ge with time).

For this the feedback is provided by voltage induced on L₁ connected in the grid circuit of valve oscillator. Whenever the magnitude of altering magnetic field increases, the length of nickel rod also increases independent of direction of magnetic field, provided it should be parallel to length of rod). Thus alternating magnetic field sets up viberations in the nickel rod such that frequency of vibration of rod is double of frequency of oscillation of magnetic field. This sitution is unwanted as amplitude of vibrations of rod will be very small in this case because the two kinds of vibrations are non resonant. To avoid this another coil L3 is wound over the rod and connected to a Polarizing d.c. supply. This produces a permanent and steady magnetic field alone one direction parallel to the length of rod. By changing current through D.C. supply, strength of steady magnetic field can be adjusted to a suitable value.When these two magnetic fields (one alternating and one steady) are super imposed, then half part of alternating magnetic field is cancelled by steady magnetic field. In this case the frequency of vibration of nickel rod will be same as that of frequency of alternating field. Thus whatever is frequency of a.c. field, same is frequency of vibration of rod.

            By changing the capacity of capacitor and by taking suitable length of nickel rod, we can produce alternating magnetic field, whose frequency matches with natural frequency of vibration of nickel rod. Due to this nickel rod shows resonant vibrations of maximum amplitude and produces ultrasonic waves of frequency at which it is vibrating. In the fundamental mode, clamped end of nickel rod acts as nod and the ends of rod act as antinodes. We know that distance between a node and antinode is ¼ of wavelength. Hence if length of rod is L, then wavelength of ultrasonic waves is given by

                                                L/2 = ¼ λ

                                                λ = 2L

The speed of ultrasonic waves in the rod is given by

                                                V = √Y/p

Where Y = Young’s modulus, p = density of nickel

The frequency of ultrasonic waves produced is given by

                        V = v/ג = 1/2L √Y/p

By varying the length of rod high frequency oscillations can be obtained. A nickle rod 10 cm long gives out ultrasonic wave of frequency = 24kHz.

This is how the ultrasonic waves are produced or generated by magnetostriction method.