12: Ultrasonics

Example number 1, Page number 394

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration
v=5750;       #velocity(m/s)
t=3*10**-3;        #thickness(m)

#Calculation
lamda=2*t;          #wavelength(m)
f=v/lamda;      #fundamental frequency(Hz)

#Result
print "fundamental frequency is",round(f/10**3,2),"KHz"
print "answer in the book varies due to rounding off errors"

fundamental frequency is 958.33 KHz
answer in the book varies due to rounding off errors

Example number 2, Page number 394

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

#Variable declaration
Y=7.9*10**10;       #youngs modulus(N/m**2)
rho=2650;           #density(Kg/m**3)
t=2*10**-3;         #thickness(m)

#Calculation
v=math.sqrt(Y/rho);    #velocity(m/s)
lamda=2*t;          #wavelength(m)
f=v/lamda;      #natural frequency(Hz)

#Result
print "natural frequency is",round(f/10**3),"KHz"

natural frequency is 1365.0 KHz
answer in the book varies due to rounding off errors

Example number 3, Page number 395

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho0=1.21;      #air density(kg/m**3)
C=343;       #sound velocity(m/sec)
f=500;       #frequency(Hz)
A=10**-5;         #displacement amplitude(m)

#Calculation
omega=2*math.pi*f;       #angular frequency(Hz)
Pe=rho0*C*omega*A;       #pressure wave amplitude(N/m**2)

#Result
print "pressure wave amplitude is",round(Pe,2),"N/m**2"

pressure wave amplitude is 13.04 N/m**2

Example number 4, Page number 395

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
Z1=1.43*10**6;      #value of constant in water(Rayls)
Z2=425.7;      #value of constant in air(Rayls)

#Calculation
Pe1byPe2=math.sqrt(Z1/Z2);     #ratio of pressure amplitudes

#Result
print "ratio of pressure amplitudes is",round(Pe1byPe2)

ratio of pressure amplitudes is 58.0