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

We known that for longitudinal waves in solids `v =sqrt((Y)/(rho))` so `v=sqrt((8xx10^(10))/(265xx10^(3)))=5.5 xx10^(3)m//s`
Further more for fundamental mode of plate `-(lamda//2)=L` So `lamda=2xx5xx10^(-3)=10^(-2)m`
But as `v = f lamda`, i.e.,`f=(v//lamda)` So `f=[5.5xx10^(3)//10^(-2)]=5.5xx10^(5)Hz=550kHz`.