# Chapter 1: Ultrasonics¶

## Example 1, Page No:1.29¶

In :
import math

# variable declaration
P           = 1;            # for fundamental mode
t           = 0.1*10**-2;    # thickness of piezo electric crystal
E           = 80*10**9       # young's modulus
p           = 2654          # density in kg/m^3

# Calculations

f           = (P/(2*t))*math.sqrt(E/p);      # frequency of the oscillator circuit

# Result
print 'The Frequency of the oscillator circuit %3.4g' %f,'Hz';

The Frequency of the oscillator circuit 2.745e+06 Hz


## Example 2, Page No:1.29¶

In :
import math
# variable declaration
P           = 1;             # for fundamental mode
t           = 0.1*10**-2;    # thickness of piezo electric crystal
E           = 7.9*10**10     # young's modulus
p           = 2650           # density in kg/m^3

# Calculations

f           = (P/(2*t))*math.sqrt(E/p);      # frequency of the oscillator circuit

#Result
print 'The Frequency of the vibrating crystal %0.2f'%(f/(10**6)),'MHz';

The Frequency of the vibrating crystal 2.73 MHz


## Example 3, Page No:1.30¶

In :
import math

# variable Declaration
f       = 1.5*10**6;         # frequency of ultrasonics in Hz
d6      = 2.75*10**-3;       # distance between 6 consecutive nodes

# Calculations
d       = d6/5;             # distance b/w two nodes
lamda   = 2*d;              #  wavelength in m
v       = f*lamda;          # velocity of ultrasonics

# Result
print 'Velocity of ultrasonics ' ,v,'m/sec';

Velocity of ultrasonics  1650.0 m/sec


## Add_example 1, Page No: 1.31¶

In :
import math

# Variable Declaration
P           = 1;            # for fundamental mode
t           = 1.5*10**-3;    # thickness of quartz crystal
E           = 7.9*10**10     # young's modulus in N/m^2
p           = 2650          # density in kg/m^3

# Calculations

f           = (P/(2*t))*math.sqrt(E/p);      # frequency of the oscillator circuit

# Result
print 'The Fundamental Frequency of the Quartz crystal %3.2f'%(f/10**6), 'MHz';

The Fundamental Frequency of the Quartz crystal 1.82 MHz


## Add_example 2, Page No: 1.31¶

In :
import math

# Variable Declaration
v       = 5000;         # velocity of ultrasonics in m/s
df      = 60*10**3;      # difference b/w two adjacent harmonic freq. in Hz

# Calculations

d       = (float(v)/(2*df))  ;       # thickness of steel plate

# Result
print 'The thickness of steel plate %3.4f'%(d),'m';

The thickness of steel plate 0.0417 m


## Add_example 3, Page No: 1.32¶

In :
import math

# Variable Declaration
v       = 1440;         # velocity of ultrasonics in  sea water in m/s
t       = 0.33          # time taken b/w tx and rx in sec

# Calculations

d       = v*t;          # distance travelled by ultrasonics
D       = d/2;          # depth of submerged submarine in m

# Result
print 'Depth of submerged submarine',D,'m';

Depth of submerged submarine 237.6 m


## Add_example 4, Page No: 1.33¶

In :
import math

# Variable Declaration
d           = 0.55*10**-3;        #  distance b/w two antinodes
f           = 1.5*10**6;         # freq of the crystal

# Calculations

lamda       = 2*d;              # wavelength
v           = f*lamda;          # velocity of ultronics

# Result
print 'Velocity of waves in sea water',v,'m/s';

Velocity of waves in sea water 1650.0 m/s


## Add_example 5, Page No: 1.33¶

In :
import math

# Variable Declaration
P           = 1;            # for fundamental mode
p           = 2660          # density of quartz in kg/m^3
f           = 1300*10**3     # freq of quartz plate for sub division ii
k           = 2.87*10**3

#f1        = (k)/t  # freq for sub division i

# Calculations

#f           = (P/(2*t))*sqrt(E/p);
E             = p*4*(k)**2;      # Youngs modulus in N/m^2
t           = (float(P)/(2*f))*math.sqrt(E/p);

# Result
print 'Youngs modulus of quartz plate %3.5g'%E,'Nm^-2'
print 'Thickness of the crystal %.4e'%t,'m';

Youngs modulus of quartz plate 8.7641e+10 Nm^-2
Thickness of the crystal 2.2077e-03 m