Ultrasonics

Example number 1.1, Page number 20

In [1]:
#To calculate the depth of a submerged submarine

#Variable declaration
v = 1440;         #velocity of ultrasonic waves(m/s)
t = 0.33;         #time elapsed(s)

#Calculation
d = v*t;      #distance travelled(m)
d1 = d/2;     #depth of submarine(m)

#Result
print "depth of the submerged submarine is",d1, "m"

depth of the submerged submarine is 237.6 m

Example number 1.2, Page number 21

In [2]:
#To calculate the natural frequency 

#importing modules
import math

#Variable declaration
l = 40;     #length of iron rod(mm)
E = 115*10**9;      #Young's modulus(N/m**2)
rho = 7.25*10**3;   #density of pure iron(kg/m**3)

#Calculation
l = l*10**-3;     #length of iron rod(m)
new = (1/(2*l))*math.sqrt(E/rho);     #natural frequency of the rod(Hz)
new = new*10**-3;             #natural frequency of the rod(kHz)
new=math.ceil(new*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "depth of the submerged submarine is",new, "kHz"

depth of the submerged submarine is 49.785 kHz

Example number 1.3, Page number 21

In [3]:
#To calculate the fundamental frequency 

#importing modules
import math

#Variable declaration
l = 1;     #length of quartz crystal(mm)
E = 7.9*10**10;      #Young's modulus(N/m**2)
rho = 2650;   #density(kg/m**3)

#Calculation
l = l*10**-3;     #length of iron rod(m)
new = (1/(2*l))*math.sqrt(E/rho);     #natural frequency of the rod(Hz)
new = new*10**-6;                   
new=math.ceil(new*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "fundamental frequency of crystal is",new, "*10**6 Hz"

fundamental frequency of crystal is 2.73 *10**6 Hz

Example number 1.4, Page number 22

In [4]:
#To calculate the velocity of waves

#importing modules
import math

#Variable declaration
d = 0.55;        #distance between 2 constructive antinodes(mm)
new = 1.5;      #frequency of crystal(MHz)
 
#Calculation
new = new*10**6;        #frequency of crystal(Hz)
d = d*10**-3;     #distance between 2 constructive antinodes(m)
#distance between 2 antinodes is given by lamda/2
lamda = 2*d;      #wavelength of ultrasonic waves(m)
v = new*lamda;       #velocity of waves(m/s)

#Result
print "velocity of waves is",int(v), "m/s"

velocity of waves is 1650 m/s

Example number 1.5, Page number 22

In [6]:
#To calculate the natural frequency

#importing modules
import math

#Variable declaration
l = 50;     #length of rod(mm)
E = 11.5*10**10;      #Young's modulus(N/m**2)
rho = 7250;   #density(kg/m**3)

#Calculation
l = l*10**-3;     #length of iron rod(m)
new = (1/(2*l))*math.sqrt(E/rho);     #natural frequency of the rod(Hz)
new = new*10**-3;       #natural frequency of the rod(kHz)
new = math.ceil(new*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "natural frequency of rod is",new, "kHz"

natural frequency of rod is 39.83 kHz

Example number 1.6, Page number 22

In [7]:
#To calculate the frequency

#importing modules
import math

#Variable declaration
l = 2;     #length of crystal(mm)
E = 7.9*10**10;      #Young's modulus(N/m**2)
rho = 2650;   #density(kg/m**3)

#Calculation
l = l*10**-3;     #length of iron rod(m)
new = (1/(2*l))*math.sqrt(E/rho);     #natural frequency of the rod(Hz)
new = new*10**-6;         #natural frequency of the rod(MHz)
new=math.ceil(new*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "frequency of crystal is",new, "MHz"

frequency of crystal is 1.365 MHz

Example number 1.7, Page number 23

In [8]:
#To calculate the frequency

#importing modules
import math

#Variable declaration
l = 3;     #length of crystal(mm)
E = 8*10**10;      #Young's modulus(N/m**2)
rho = 2500;   #density(kg/m**3)

#Calculation
l = l*10**-3;     #length of iron rod(m)
new = (1/(2*l))*math.sqrt(E/rho);     #natural frequency of the rod(Hz)
new = new*10**-3;         #natural frequency of the rod(kHz) 
new=math.ceil(new*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "frequency of crystal is",new, "kHz"

frequency of crystal is 942.81 kHz

Example number 1.8, Page number 23

In [9]:
#To calculate the frequency

#importing modules
import math

#Variable declaration
l = 1.5;     #length of crystal(mm)
E = 7.9*10**10;      #Young's modulus(N/m**2)
rho = 2650;   #density(kg/m**3)

#Calculation
l = l*10**-3;     #length of iron rod(m)
new = (1/(2*l))*math.sqrt(E/rho);     #natural frequency of the rod(Hz)
new = new*10**-6;         #natural frequency of the rod(MHz) 
new=math.ceil(new*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "frequency of crystal is",new, "MHz"

frequency of crystal is 1.82 MHz

Example number 1.9, Page number 24

In [10]:
#To calculate the depth of the sea

#Variable declaration
v = 1440;         #velocity of ultrasonic waves(m/s)
t = 0.95;         #time elapsed(s)

#Calculation
d = v*t;      #distance travelled(m)
d1 = d/2;     #depth of sea(m)

#Result
print "depth of the submerged submarine is",int(d1), "m"

depth of the submerged submarine is 684 m

Example number 1.10, Page number 24

In [11]:
#To calculate the depth of a submerged submarine

#Variable declaration
v = 1440;         #velocity of ultrasonic waves(m/s)
t = 0.83;         #time elapsed(s)

#Calculation
d = v*t;      #distance travelled(m)
d1 = d/2;     #depth of submarine(m)

#Result
print "depth of the submerged submarine is",d1, "m"

depth of the submerged submarine is 597.6 m

Example number 1.11, Page number 24

In [13]:
#To calculate the reverberation time of hall

#importing modules
import math

#Variable declaration
aS = 1050;      #total absorption inside hall(Sabine)
V = 9000;       #volume of cinema hall(m**3)

#Calculation
T = 0.165*V/aS;     #reverberation time of hall(s)
T = math.ceil(T*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "reverberation time of the hall is",T, "s"

reverberation time of the hall is 1.4143 s

Example number 1.12, Page number 25

In [14]:
#To calculate the area of interior surface

#importing modules
import math

#Variable declaration
a = 0.65;      #average absorption coefficient(Sabine/m**2)
V = 13500;       #volume of auditorium(m**3)
T = 1.2;         #reverberation time of hall(s)

#Calculation
S = 0.165*V/(a*T);     #reverberation time of hall(s)
S = math.ceil(S*10)/10;   #rounding off to 1 decimal

#Result
print "total area of interior surface is",S, "m**2"

total area of interior surface is 2855.8 m**2

Example number 1.13, Page number 25

In [16]:
#To calculate the new reverberation time of hall

#importing modules
import math

#Variable declaration
V = 15000;       #volume of cinema hall(m**3)
T1 = 1.3;        #initial reverberation time of hall(s)
a1S1 = 300;      #number of chairs placed

#Calculation
aS = 0.165*V/T1;         #total absorption of hall
T2 = (0.165*V)/(aS+a1S1);      #reverberation time of hall after adding chairs(s)
T2 = math.ceil(T2*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "reverberation time of the hall after adding chairs is",T2, "s"

reverberation time of the hall after adding chairs is 1.1231 s

Example number 1.14, Page number 26

In [17]:
#To calculate the depth of a submerged submarine

#Variable declaration
v = 1440;         #velocity of ultrasonic waves(m/s)
t = 0.5;         #time elapsed(s)

#Calculation
d = v*t;      #distance travelled(m)
d1 = d/2;     #depth of submarine(m)

#Result
print "depth of the submerged submarine is",int(d1), "m"

depth of the submerged submarine is 360 m

Example number 1.15, Page number 26

In [18]:
#To calculate the velocity of waves

#importing modules
import math

#Variable declaration
d = 0.4;        #distance between 2 constructive antinodes(mm)
new = 1.5;      #frequency of crystal(MHz)
 
#Calculation
new = new*10**6;        #frequency of crystal(Hz)
d = d*10**-3;     #distance between 2 constructive antinodes(m)
#distance between 2 antinodes is given by lamda/2
lamda = 2*d;      #wavelength of ultrasonic waves(m)
v = new*lamda;       #velocity of waves(m/s)

#Result
print "velocity of waves is",int(v), "m/s"

velocity of waves is 1200 m/s

Example number 1.16, Page number 26

In [19]:
#To calculate the natural frequency 

#importing modules
import math

#Variable declaration
l = 40;     #length of iron rod(mm)
E = 11.5*10**10;      #Young's modulus(N/m**2)
rho = 7250;   #density of pure iron(kg/m**3)

#Calculation
l = l*10**-3;     #length of iron rod(m)
new = (1/(2*l))*math.sqrt(E/rho);     #natural frequency of the rod(Hz)
new = new*10**-3;             #natural frequency of the rod(kHz)
new=math.ceil(new*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "depth of the submerged submarine is",new, "kHz"

depth of the submerged submarine is 49.785 kHz
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