Question

Tank circuit of magnetostriction generator is having capacitance of 1 $\mu$F and inductance 10mH. If the velocity of ultrasonic in this medium is 2000m/s and ultrasonic vibration is taking place along the length of material, calculate the length of this magnetostriction material.

Answer 1

0.628 m

Answer 2

The resonant frequency of the LC circuit is $f = \frac{1}{2\pi\sqrt{LC}}$. The fundamental longitudinal resonant frequency of the magnetostriction material is $f = \frac{v}{2l}$. Equating these frequencies for resonance gives $\frac{1}{2\pi\sqrt{LC}} = \frac{v}{2l}$. Solving for $l$ yields $l = \pi v \sqrt{LC}$. Substituting the given values: $L = 10 \times 10^{-3}$ H, $C = 1 \times 10^{-6}$ F, and $v = 2000$ m/s. Thus, $l = \pi \times 2000 \times \sqrt{(10 \times 10^{-3}) \times (1 \times 10^{-6})} = \pi \times 2000 \times \sqrt{10^{-8}} = \pi \times 2000 \times 10^{-4} = 0.2\pi \approx 0.628$ m.