# 5: Ultrasonics¶

## Example number 5.1, Page number 23¶

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
t=1*10**-3;   #thickness of crystal(m)
rho=2650;   #density of quartz(kg/m**3)
Y=7.9*10**10;   #young's modulus(N/m**2)
p=1;

#Calculation
f=(p/(2*t))*math.sqrt(Y/rho);   #fundamental frequency(Hz)

#Result
print "fundamental frequency is",round(f/10**6,5),"*10**6 Hz"

fundamental frequency is 2.72999 *10**6 Hz


## Example number 5.2, Page number 23¶

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
t=5*10**-3;    #length of crystal(m)
Y=7.9*10**10;   #young's modulus(N/m**2)
p1=1;
p2=2;
rho=2650;   #density of quartz(kg/m**3)

#Calculation
f1=(p1/(2*t))*math.sqrt(Y/rho);   #fundamental frequency(Hz)
f2=(p2/(2*t))*math.sqrt(Y/rho);   #frequency of 1st overtone(Hz)

#Result
print "fundamental frequency is",round(f1/10**5,2),"*10**5 Hz"
print "frequency of 1st overtone is",round(f2/10**6,3),"*10**6 Hz"

fundamental frequency is 5.46 *10**5 Hz
frequency of 1st overtone is 1.092 *10**6 Hz


## Example number 5.3, Page number 24¶

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
u=5000;   #velocity of sound in steel(m/s)
f=50*10**3;   #difference between frequencies(Hz)

#Calculation
d=u/(2*f);   #thickness of steel plate(m)

#Result
print "thickness of steel plate is",d,"m"

thickness of steel plate is 0.05 m


## Example number 5.4, Page number 25¶

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
t=1;   #assume
f1=(2.87*10**3)/t;   #fundamental frequency(Hz)
f=1200*10**3;     #frequency(Hz)
rho=2660;   #density of quartz(kg/m**3)

#Calculation
Y=rho*(f1*2*t)**2;   #young's modulus(N/m**2)
t1=(1/(2*f))*math.sqrt(Y/rho);   #thickness of crystal(m)

#Result
print "young's modulus is",round(Y/10**10,3),"*10**10 N/m**2"
print "thickness of crystal is",round(t1*10**3,2),"*10**-3 m"

young's modulus is 8.764 *10**10 N/m**2
thickness of crystal is 2.39 *10**-3 m


## Example number 5.5, Page number 26¶

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
f=7*10**6;    #ultrasonic frequency(Hz)
theta=45;   #transducer angle(degrees)
v=1.5;    #blood velocity(m/s)
U=1500;   #ultrasonic velocity(m/s)

#Calculation

audio frequency is 10.0 kHz