Final answer:
The fundamental frequency of a piezoelectric crystal with a thickness of 0.001 m and a sound wave velocity of 6000 m/s is 3 MHz.
Step-by-step explanation:
To calculate the fundamental frequency of a piezoelectric crystal, we can use the relationship that the frequency (f) is equal to the speed of sound (v) divided by twice the thickness (d) of the crystal, assuming the first harmonic corresponds to the thickness being half a wavelength. This is expressed as: f = v / (2d)
Given that the velocity of sound waves is 6000 m/s and the thickness of the piezoelectric crystal is 0.001 m, we can plug these values into the formula: f = 6000 m/s / (2 × 0.001 m)
Therefore, the fundamental frequency is: f = 6000 m/s / 0.002 m f = 3 × 106 Hz
The fundamental frequency of the piezoelectric crystal is 3 MHz (megahertz).