Question

A piezo electric quartz crystal of thickness 0.005 m is vibrating in resonate conditions. Calculate the fundamental frequency f₀ for quartz Y = 8 × 10¹⁰Nm^–2 and r = 2.65 × 10³ kgm^–3

• A. 5.5 MHz
• B. 55 MHz
• C. 0.55 MHz
• D. 5.5 kHz

Answer 1

Answer: (B)

55 MHz

Answer 2

dB = 10 log $\left\lbrack \frac{I}{I_{0}} \right\rbrack$ = 10 log $\left\lbrack \frac{K/r^{2}}{I_{0}} \right\rbrack$

= 10 [log (K') –2 log r]

dB₁ = 10 (log K' –2 log r₁)

dB₂ = 10 (log K' –2 log r₂)

3 = dB₁ – dB₂ = 20 log $\left\lbrack \frac{r_{2}}{r_{1}} \right\rbrack$ Ž (0.3) = log$\left\lbrack \frac{r_{2}}{r_{1}} \right\rbrack^{2}$

Ž $\left( \frac{r_{1}}{r_{2}} \right)$ = $\frac{1}{\sqrt{2}}$