# chapter6 :Ultrasonic Waves¶

## example 6.1;page no:262¶

In :
#cal of Fundamental frequency
#intiation of all variables
#Given that
import math
E=7.9*10**10
rho = 2650 # Density in Kg/m**3
t = 0.003 # Thickness of quartz crystal in m
print("Example 6.1,page no:262")
v = math.sqrt(E/rho)# Calculation of velocity
lamda = 2*t # Calculation of fundamental wavelength
nu = v/lamda # Calculation of fundamental frequency
print("Fundamental frequency in Hz in 10^5:"),round(nu/10**5,5)

Example 6.1,page no:262
Fundamental frequency in Hz in 10^5: 9.09996


# example 6.2;page no:263¶

In :
#cal of Fundamental frequency of crystal
#intiation of all variables
#Given that
v = 5760 # Velocity in m/s
T = 1.6 # Thickness of quartz crystal in mm
print("Example 6.2,page no:263")
nu = v/(2*T*1e-3)# Calculation of fundamental frequency
print("Fundamental frequency of crystal in MHz:"),round(nu/1e6,1)

Example 6.2,page no:263
Fundamental frequency of crystal in MHz: 1.8


## example 6.3;page no:264¶

In :
#cal of Depth of defect
#intiation of all variables
#Given that
T =40 # Thickness of steel bar in cm
t1 = 40 # Time in ms
t2 = 80 # Time in ms
print("Example 6.3,page no:264")
X = T*t1/t2 # Calculation of depth of defect
print("Depth of defect in cm:"),X

Example 6.3,page no:264
Depth of defect in cm: 20


# example 6.4;page no:264¶

In :
#cal of Fundamental frequency
#intiation of all variables
#Given that
import math
E=7.9*10**10
rho = 2650 # Density in Kg/m**3
t = 0.006 # Thickness of quartz crystal in m
print("Example 6.4,page no:264")
v = math.sqrt(E/rho)# Calculation of velocity
lamda = 2*t # Calculation of fundamental wavelength
nu = v/lamda # Calculation of fundamental frequency
print("Fundamental frequency in Hz in 10^5:"),round(nu/10**5,5)

Example 6.4,page no:264
Fundamental frequency in Hz in 10^5: 4.54998


## example 6.5;page no:265¶

In :
#cal of Capacitance
#intiation of all variables
#Given that
import  math
L = 1 # Inductance in Hanery
nu = 2e6 # Frequency in Hz
print("Example 6.5,page no:265")
C= 1/(4*((math.pi)**2)*nu**2*L) # Calculation of capacitance
print("Capacitance in microfarad:"),round(C*1e6,5)
# Answer in book is 0.00634 micro Farad

Example 6.5,page no:265
Capacitance in microfarad: 0.0