# 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