# Ultrasonics¶

## Example number 1.1, Page number 28¶

In :
#importing modules
import math

#Variable declaration
t=0.15*10**-2;        #thickness of the quartz crystal in m
Y=7.9*10**10;         #young's modulus of quartz in N/m^2
rho=2650;          #density of quartz in kg/m^3

#Calculation
x=math.sqrt(Y/rho);
f=x/(2*t);
f=f*10**-6;        #converting f from Hz to MHz
f=math.ceil(f*10**6)/10**6;   #rounding off to 6 decimals

#Result
print("fundamental frequency of vibration in MHz is",f);

('fundamental frequency of vibration in MHz is', 1.819992)


## Example number 1.2, Page number 28¶

In :
#importing modules
import math

#Variable declaration
t=1e-03;        #thickness of the quartz crystal in m
Y=7.9*10**10;       #young's modulus of quartz in N/m^2
rho=2650;          #density of quartz in kg/m^3

#Calculation
x=math.sqrt(Y/rho);
p1=1;        #for fundamental frequency p=1
f1=(p1*x)/(2*t);
F1=f1/10**6;
F1=math.ceil(F1*10**5)/10**5;   #rounding off to 5 decimals
f_1=f1*10**-6;      #converting f1 from Hz to MHz
f_1=math.ceil(f_1*10**5)/10**5;   #rounding off to 5 decimals
p2=2;       #for first overtone p=2
f2=(p2*x)/(2*t);
F2=f2/10**6;
F2=math.ceil(F2*10**5)/10**5;   #rounding off to 5 decimals
f_2=f2*10**-6;      #converting f2 from Hz to MHz
f_2=math.ceil(f_2*10**5)/10**5;   #rounding off to 5 decimals

#Result
print("fundamental frequency in Hz is",F1,"*10**6");
print("fundamental frequency in MHz is",f_1);
print("frequency of the first overtone in Hz is",F2,"*10**6");
print("frequency of the first overtone in MHz is",f_2);

('fundamental frequency in Hz is', 2.72999, '*10**6')
('fundamental frequency in MHz is', 2.72999)
('frequency of the first overtone in Hz is', 5.45998, '*10**6')
('frequency of the first overtone in MHz is', 5.45998)


## Example number 1.3, Page number 29¶

In :
#importing modules
import math

#Variable declaration
lamda=589.3*10**-9;       #wavelength of light in m
f=100*10**6;       #frequency of ultrasonic transducer in Hz
n=1;       #order of diffraction
theta=2.25;          #angle of diffraction in degrees
theta=theta*0.0174532925;       #converting degrees to radians

#Calculation
d=(n*lamda)/(2*math.sin(theta));
d1=d*10**6;      #converting d from m to micro m
lamda1=2*d;
v=f*lamda1;
v=math.ceil(v*100)/100;   #rounding off to 2 decimals

#Result
print("wavelength of ultrasonic wave in m is",lamda1);
print("velocity of ultrasonic wave in m/sec",int(v));

('wavelength of ultrasonic wave in m is', 1.5010258944908707e-05)
('velocity of ultrasonic wave in m/sec', 1501)


## Example number 1.4, Page number 29¶

In :
#importing modules
import math

#Variable declaration
f=2*10**6;      #frequency of transducer in MHz
v=3;       #speed of blood in m/s
c=800;      #velocity of ultrasonic wave in m/s
theta=30;       #angle of inclination in degrees
theta=theta*0.0174532925;       #converting degrees to radians

#Calculation
deltaf=(2*f*v*math.cos(theta))/c;
deltaf=deltaf*10**-6;       #converting deltaf from Hz to MHz
deltaf=math.ceil(deltaf*10**6)/10**6;   #rounding off to 6 decimals

#Result
print("doppler shifted frequency in MHz is",deltaf);

('doppler shifted frequency in MHz is', 0.012991)


## Example number 1.5, Page number 30¶

In :
#importing modules
import math

#Variable declaration
Y=7.9*10**10;         #young's modulus of quartz in N/m^2
rho=2650;          #density of quartz in kg/m^3

#Calculation
v=math.sqrt(Y/rho);
v=math.ceil(v*10**3)/10**3;   #rounding off to 3 decimals

#Result
print("velocity of ultrasonic waves in m/s is",v);

('velocity of ultrasonic waves in m/s is', 5459.975)

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