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"
```

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"
```

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"
```

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"
```

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"
```

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
```

In [ ]:

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