18: Acoustics of Buildings

Example number 18.1, Page number 361

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
r = 200;       #Distance of the point of reduction from the source(m)
I_0 = 10**-12;    #Final intensity of sound(W/m**2)
I_f = 60;        #Intensity gain of sound at the point of reduction(dB)

#Calculation
#As A_I = 10*log10(I/I_0), solving for I
I = I_0*10**(I_f/10);      #Initial Intensity of sound(W/m**2)
P = 4*math.pi*r**2*I;      #Output power of the sound source(W)
P = math.ceil(P*100)/100;     #rounding off the value of P to 2 decimals

#Result
print "The output power of the sound source is",P, "W"

The output power of the sound source is 0.51 W

Example number 18.2, Page number 361

In [3]:
#importing modules
import math
from __future__ import division
import numpy as np

#Variable declaration
I1 = 1;    #For simplicity assume first intensity level to be unity(W/m**2)

#Calculation
I2 = 2*I1;    #Intensity level after doubling(W/m**2)
dA_I = 10*np.log10(I2/I1);    #Difference in gain level(dB)

#Result
print "The sound intensity level is increased by",int(dA_I), "dB"

The sound intensity level is increased by 3 dB

Example number 18.3, Page number 361

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

#Variable declaration
V = 8000;    #Volume of the hall(m**3)
T = 1.5;     #Reverbration time of the hall(s)

#Calculation
alpha_s = 0.167*V/T;     #Sabine Formula giving total absorption of sound in the hall(OWU)
alpha_s = math.ceil(alpha_s*10)/10;     #rounding off the value of alpha_s to 1 decimal

#Result
print "The total absorption of sound in the hall is",alpha_s, "OWU"

The total absorption of sound in the hall is 890.7 OWU

Example number 18.4, Page number 362

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
V = 25*20*8;       #Volume of the hall(m**3)
T = 4;     #Reverbration time of the hall(s)

#Calculation
S = 2*(25*20+25*8+20*8);    #Total surface area of the hall(m**2)
alpha = 0.167*V/(T*S);     #Sabine Formule giving total absorption in the hall(OWU)
alpha = math.ceil(alpha*10**4)/10**4;     #rounding off the value of alpha to 4 decimals

#Result
print "The average absorption coefficient of the surfaces is",alpha, "OWU/m**2"

The average absorption coefficient of the surfaces is 0.0971 OWU/m**2

Example number 18.5, Page number 362

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
V = 475;      #Volume of the hall(m**3)
A_f = 100;     #Area of the floor(m**2)
A_c = 100;     #Area of the ceiling(m**2)
A_w = 200;     #Area of the wall(m**2)
alpha_w = 0.025;     #Absorption coefficients of the wall(OWU/m**2)
alpha_c = 0.02;      #Absorption coefficients of the ceiling(OWU/m**2)
alpha_f = 0.55;      #Absorption coefficients of the floor(OWU/m**2)

#Calculation
alpha_s = (A_w*alpha_w)+(A_c*alpha_c)+(A_f*alpha_f);    
T = 0.167*V/alpha_s;    #Sabine Formula for reverbration time(s)
T = math.ceil(T*100)/100;     #rounding off the value of T to 2 decimals

#Result
print "The reverbration time for the hall is",T, "s"

The reverbration time for the hall is 1.28 s

Example number 18.6, Page number 362

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

#Variable declaration
I0 = 1;    #For simplicity assume initial sound intensity to be unity(W/m**2)
A_I1 = 80;   #First intensity gain of sound(dB)
A_I2 = 70;   #Second intensity gain of sound(dB)

#Calculation
#As A_I = 10*log10(I/I_0), solving for I1 and I2
I1 = 10**(A_I1/10)*I0;    #First intensity of sound(W/m**2)
I2 = 10**(A_I2/10)*I0;    #Second intensity of sound(W/m**2)
I = I1 + I2;     #Resultant intensity level of sound(W/m**2)
A_I = 10*np.log10(I/I0);    #Intensity gain of resultant sound(dB)
A_I = math.ceil(A_I*10**3)/10**3;     #rounding off the value of A_I to 3 decimals

#Result
print "The intensity gain of resultant sound is",A_I, "dB"

#answer given in the book is wrong

The intensity gain of resultant sound is 80.414 dB
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