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A piezoelectric quartz plate of thicknes...

A piezoelectric quartz plate of thickness 5mm is vibrating is resonance. Calculate its fundamental frequency if for quartz.
`Y=8xx10^(10)N//m^(2)` and `rho=2.65xx10^(3)kg//m^(3)`.

Text Solution

Verified by Experts

L = 5 mm `= 5 xx 10^(-3)` m
v = ?
`Y = 800 xx 10^(8) N//m^(2)`
`rho = 27 xx 10^(8) kg//m^(3)`
`V = sqrt((Y)/(rho)) = sqrt((800 xx 10^(8))/(27 xx 10^(2))) = 5.4 xx 10^(3)` m/s
In fundamental mode of vibration
We can say `lambda = 2L = 2 xx 5 xx 10^(-3)` m
`= 10 xx 10^(-3)` m
frequency `= (V)/(lambda) = (5.4 xx 10^(3))/(10 xx 10^(-3))`
`= 0.54 xx 10^(6)` Hz
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