Understanding the Basics
* Piezoelectric Effect: Quartz crystals exhibit the piezoelectric effect, meaning they generate an electric charge when subjected to mechanical stress (like vibration). Conversely, applying an electric field causes them to deform. This property is crucial for their use in oscillators.
* Fundamental Frequency: The fundamental frequency is the lowest frequency at which a crystal will naturally vibrate. It depends on the crystal's length and the speed of sound within the crystal.
Formula
The fundamental frequency (f) of a piezoelectric crystal can be calculated using the following formula:
f = v / (2 * L)
Where:
* f = Fundamental frequency (Hz)
* v = Velocity of longitudinal waves in the crystal (m/s)
* L = Length of the crystal (m)
Calculations
1. Given Values:
* L = 0.05 m
* v = 5.5 x 1000 m/s
2. Substitute the values into the formula:
f = (5.5 x 1000 m/s) / (2 * 0.05 m)
3. Calculate the result:
f = 55,000 Hz
Therefore, the fundamental frequency of oscillation for a quartz crystal with a length of 0.05 meters and a longitudinal wave velocity of 5.5 x 1000 m/s is 55,000 Hz (or 55 kHz).
