In [1]:

```
#Variable declaration
d = 8e-004; # Thickness of the piece of piezoelectric crystal, m
v = 5760; # Velocity of ultrasonic waves in the piece of piezoelectric crystal, m/s
#Calculations
n = v/(2*d); # The frequency of the fundamental mode of ultrasonic wave, Hz
#Result
print "The frequency of the fundamental mode of ultrasonic wave = %3.1f MHz"%(n/1e+006)
```

In [2]:

```
from math import *
#Variable declaration
d = 2e-003; # Thickness of the piece of quarts crystal, m
rho = 2650; # Density of the crystal, kg/meter-cube
Y = 7.9e+010; # Value of Youngs Modulus, N/metre-square
#Calculations
n = 1/(2*d)*sqrt(Y/rho); #The frequency of the fundamental mode of vibration, Hz
#Result
print "The frequency of the fundamental mode of vibration in quatrz crystal = %5.3f Hz"%(n/1e+006)
```

In [3]:

```
#Variable declaration
v = 5e+003; # Velocity of ultrasonic beam in steel plate, m/s
n = 25e+003; # Difference between two neighbouring harmonic frequencies (Nm - Nm_minus1), Hz
#Calculations
d = v/(2*n); # The thickness of steel plate, m
#Result
print "The thickness of steel plate = %3.1f m"%d
```

In [4]:

```
from math import *
#Variable declaration
n = 1e+006; # Frequency of Ultrasonic waves, Hz
C = 2.5e-014; # Capcitance of capacitor, F
#Calculations
# Frequency of elecric oscillations is given by n = 1/(2*%pi)*sqrt(1/(L*C)), solving for L
L = 1/(4*pi**2*n**2*C); # The inductance of an inductor to produce ultrasonic waves, henry
#Result
print "The inductance of an inductor to produce ultrasonic waves = %d henry"%L
```

In [6]:

```
#Variable declaration
d = 50e-002; # Thickness of the metallic rod, m
t1 = 30e-006; # Arrival time for first pulse, s
t2 = 80e-006; # Arrival time for second pulse, s
#Calculations&Results
v = 2*d/t2; # Velocity of ultrasonic waves, m/s
print "The velocity of pulse inside the rod = %4.2e m/s"%v
x = t1*v/2;
print "The position of pulse inside the rod = %6.4f m"%x
```

In [8]:

```
from math import *
#Variable declaration
I = 2.5e+004; # Sound intensity, W/meter-square
v = 1480; # Sound velocity, m/s
rho_w = 1000; # Density of water, kg/meter-cube
rho_c = 2650; # Density of crystal of transducer, kg/meter-cube
d = 0.001; # Thickness of the quartz, m
f = 20e+003; # Frequency of sound in water, Hz
#Calculations&Results
# As sound intensity, I = p^2/(2*rho1*v), solving for p
p = sqrt(2*rho_w*v*I); # Pressure in the medium, N/metre-square
a = p/(d*rho_c); # Maximum acceleration of the quartz ultrasonic transducer, metre/second-square
print "The maximum acceleration produced in quartz transducer = %4.2e metre/second-square"%a
y = a/(2*pi*f)**2; # Maximum displacement of the quartz transducer, m
print "The maximum displacement of quartz transducer = %3.1f micrometer"%(y/1e-006)
```

In [9]:

```
#Variable declaration
L = 0.2; # Length of a magnetostrictive hydrophone, m
lamda = 2*L; # Wavelength of ultrasonic wave, m
v = 4900; # Velocity of ultrasonic beam in water, m/s
#Calculations
f = v/lamda; # Fundamental frequency of ultrasonic, KHz
#Result
print "The fundamental frequency of a magnetostrictive hydrophone = %4.2f KHz"%(f/1e+03)
```

In [10]:

```
#Variable declaration
v = 3700; # Velocity of ultrasonic beam in copper, m/s
t = 1e-006; # Delay time for ultrasonic beam, s
#Calculations
L = v*t; # # Length of a copper wire required for a delay, m
#Result
print "The length of a copper wire required for a delay = %6.4f m"%L
```