# 2: Ultrasonics¶

## Example number 2.1, Page number 30¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
E=80*10**9;    #Young's modulus of material of piezo electric crystal(Pa)
d=2654;    #Density of material of piezo electric crystal(Kg/m^3)
t=0.1*10**-2;   #Thickness of  piezo electric crystal(m)
p=1;    #for fundamental first overtone

#Calculation
f=((p/(2*t))*(math.sqrt(E/d)));    #Frequency of vibration of first overtone(Hz)

#Result
print "The frequency of vibration is",round(f/10**6,4),"*10**6 Hz"

The frequency of vibration is 2.7451 *10**6 Hz


## Example number 2.2, Page number 30¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
v=5.5*10**3;     #Velocity of longitudanal waves in Quartz Crystal(m/s)
t=0.05;    #Thickness of Quartz Crystal(m)

#Calculation
w=2*t;     #wavelength(m)
v1=(v/w);    #Frequency in the first mode of vibration(Hz)
v2=(2*v1);   #Frequency in the second mode of vibration(Hz)

#Result
print "Frequency in the first mode of vibration is",v1/10**4,"*10**4 Hz"
print "Frequency in the second mode of vibration is",v2/10**3,"*10**3 Hz"

Frequency in the first mode of vibration is 5.5 *10**4 Hz
Frequency in the second mode of vibration is 110.0 *10**3 Hz


## Example number 2.3, Page number 31¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
f=0.09*10**6;    #Frequency of Ultrasonic source(Hz)
t=0.55;     #time(sec)
v=1800;     #velocity of sound in water(m/s)

#Calculation
D=(v*t)/2;    #Depth of sea(m)
W=(v/f);      #Wavelength of ultrasonic pulse(m)

#Result
print "The depth of sea is",D,"m"
print "The wavelength of ultrasonic pulse is",W,"m"

The depth of sea is 495.0 m
The wavelength of ultrasonic pulse is 0.02 m