In [1]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
f = 3; #Fundamental vibrational frequency of quartz crystal(MHz)
Y = 7.9*10**10; #Young's modulus of quartz(N/m**2)
rho = 2650; #Density of quartz(kg/m**3)
#Calculation
f = f*10**6; #Fundamental vibrational frequency of quartz crystal(Hz)
l = 1/(2*f)*math.sqrt(Y/rho); #Thickness of vibrating quartz at resonance(m)
l = l*10**3; #Thickness of vibrating quartz at resonance(mm)
l = math.ceil(l*100)/100; #rounding off the value of l to 2 decimals
#Result
print "The thickness of vibrating quartz at resonance is",l, "mm"
```

In [ ]:

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