Question

A piezoelectric transducer is directly connected through a cable to an electronic voltmeter. The minimum operating frequency of measurement is 1000 Hz. If the connecting cable length is doubled, the new minimum operating frequency is

• A. 500 Hz
• B. 1000 Hz
• C. 2000 Hz
• D. 4000 Hz

Answer 1

The correct option is A 500 Hz


$C=\frac{A{\epsilon }_0}{d}$

$\therefore C\propto A$

$\therefore C_{new}=2C_{old}$

$\therefore X_c=\frac{1}{\omega C}\Rightarrow \omega =\frac{1}{X_{c}C}$

$\therefore f\propto \frac{1}{C}$

$\frac{1}{f_{new}}=2\times \frac{1}{f_{old}}$

$f_{new}=\frac{f_{old}}{2}=\frac{1000}{2}=500Hz$