Given Young's modulus of quartz $Y = 8 × 10^{10} N/m^2$, density is 2650 $kg/m^3$. Calculate the change in thickness required if the same plate is used to produce ultrasonic waves of frequency 3MHz.

Given:-

$t_0 = 2mm$ (Thickness of plate)

$Y = 8 × 10^{10} N/m^2$

$ρ = 2650 kg/m^3$

$f = 3 MHz = 3 ×10^6 MHz$

To find: -

Original Natural Frequency $(f_0)$

Change in thickness (∆t) for f = 3 MHz

Solution:-

1. Original Natural Frequency:-

$$f_0 = \frac{1}{2t_0}\sqrt{\frac{Y}{ρ}}$$

$$ ∴ …