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)`.

Explanation

Her, `L=5mm=5xx10^(-3)m,v=?`
`Y=8xx10^(10)N//m^(2), rho=2.65xx10^(3)kg//m^(3)`
From `v=sqrt((Y)/(rho))=sqrt((8xx10^(10))/(2.65xx10^(3)))=5.5xx10^(3)m//s`
In fundamental mode of vibration,
`lambda=2L=2xx5xx10^(-3)m =10^(-2)m.`
`v=(upsilon)/(lambda)=(5.5xx10^(3))/(10^(-2))=5.5xx10^(5)Hz`