# 1: Acoustics¶

## Example number 1.1, Page number 2¶

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

#Variable declaration
i=20;     #the intensity of a source is increased 20 times

#Calculation
I=(10*(math.log10(i)));    #intensity of sound(dB)

#Result
print "The sound intensity level is imcreased by",round(I,2),"dB when the intensity is doubled"

The sound intensity level is imcreased by 13.01 dB when the intensity is doubled


## Example number 1.2, Page number 2¶

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

#Variable declaration
i=4;   #the intensity of a source is increased 4 times

#Calculation
I=(10*(math.log10(i)));    #intensity of sound(dB)

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

The sound intensity level is increased by 6 dB


## Example number 1.3, Page number 2¶

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

#Variable declaration
I=1000;   #sound intensity of plane leaving the runway(Wm**-2)
Io=10**-12;    #threshold intensity of sound(Wm**-2)

#Calculation
IL=(10*math.log10(I/Io));   #The intensity level of a plane just leaving the runway(dB)

#Result
print "The intensity level of a plane just leaving the runway is",IL,"dB"

The intensity level of a plane just leaving the runway is 150.0 dB


## Example number 1.4, Page number 2¶

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

#Variable declaration
I=10**-6;     #intensity of sound during heavy traffic(Wm**-2)
Io=10**-12;   #threshold intensity of sound(Wm**-2)

#Calculation
IL=(10*math.log10(I/Io));    #The intensity level(dB)

#Result
print "The intensity level is",IL,"dB"

The intensity level is 60.0 dB


## Example number 1.5, Page number 3¶

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

#Variable declaration
Q=3.56;     #rate of energy radiates(W)
r=15;    #distance of intensity level(m)
Io=100;  #reference intensity(Wm^-2)

#Calculation
A=4*math.pi*r**2;    #Area(m^2)
I=(Q/A);    #sound intensity(Wm^-2)
IL=(10*math.log10(I/Io));    #The intensity level(dB)

#Result
print "The intensity level is",round(IL,4),"dB"
print "answer varies due to rounding off errors"

The intensity level is -48.9994 dB
answer varies due to rounding off errors


## Example number 1.6, Page number 3¶

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
Il1=70;   #sound(dB)
Il2=80;   #sound(dB)

#Calculation
I1=10**(Il1/10);    #ratio of intensity
I2=10**(Il2/10);    #ratio of intensity
I=I1+I2;    #intensity of sound(dB)
Il=10*math.log10(I);   #resultant intensity(dB)

#Result
print "The resultant sound level is",round(Il,2),"dB"

The resultant sound level is 80.41 dB


## Example number 1.7, Page number 4¶

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
i=4;   #the intensity of a source
I1=95;  #The noise level of sound from a drill(dB)

#Calculation
I2=(10*(math.log10(i)));    #intensity of source(dB)
IL=I1+I2;    #The noise level at this point(dB)

#Result
print "The noise level at the point when 4 such drills are working at the same distance away is",round(IL,2),"dB"

The noise level at the point when 4 such drills are working at the same distance away is 101.02 dB


## Example number 1.8, Page number 4¶

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
f=426;    #frequency of sound(Hz)
a=0.65*10**-2;   #amplitude of sound wave(m)
A=1;     #area(m^2)
v=340;   #velocity of sound in air(ms^-1)
d=1.29;  #density of air(Kgm^-3)

#Calculation
I=(2*math.pi**2*f**2*a**2*d*v);     #The flow of energy across 1m^2 per second(Wm^-2*10^4)

#Result
print "The flow of energy across 1m^2 per second is",round(I/10**4,3),"*10**4 Wm**-2"
print "answer varies due to rounding off errors"

The flow of energy across 1m^2 per second is 6.638 *10**4 Wm**-2
answer varies due to rounding off errors


## Example number 1.9, Page number 12¶

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

#Variable declaration
V=1000;     #volume of hall(m^3)
S=400;   #sound absorbing surface of area(m^2)
a=0.2;   #average absorption coefficient(sabine)

#Calculation
T=(0.167*V)/(a*S);    #The reverberation time of the hall(sec)

#Result
print "The reverberation time of the hall is",round(T,3),"sec"

The reverberation time of the hall is 2.087 sec


## Example number 1.10, Page number 12¶

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

#Variable declaration
V=1500;    #volume of room(m^3)
a1=0.03;   #average sound coefficient for wall(sabine)
a2=0.06;   #average sound coefficient for the ceiling(sabine)
a3=0.8;    #average sound coefficient for the floor(sabine)
S1=260;    #The wall area of the room(m^2)
S2=140;    #The floor area of the room(m^2)
S3=140;    #The ceiling area of the room(m^2)

#Calculation
a=((a1*S1)+(a2*S2)+(a3*S3))/(S1+S2+S3);     #The average absorbtion coefficient(O.W.U)
TS=S1+S2+S3;     #total area of the room(m^2)
x=(a*TS);      #Total sound absorbtion of the room(O.W.U m^2)
T=((0.167*V)/x);   #The reverberation time(sec)

#Result
print "The average absorbtion coefficient is",round(a,4),"O.W.U"
print "Total sound absorbtion of the room is",x,"O.W.U m^2"
print "answer varies due to rounding off errors"
print "The reverberation time is",round(T,3),"sec"

The average absorbtion coefficient is 0.2374 O.W.U
Total sound absorbtion of the room is 128.2 O.W.U m^2
answer varies due to rounding off errors
The reverberation time is 1.954 sec


## Example number 1.11, Page number 13¶

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

#Variable declaration
V=12000;   #volume of auditorium(m^3)
T=1.5;    #The reverberation time of the auditorium(sec)
a=0.4;    #average absorption coefficient(sabine)

#Calculation
S=(0.167*V)/(a*T);      #area of interior surfaces(m^2)

#Result
print "The area of interior surfaces is",S,"m**2"

The area of interior surfaces is 3340.0 m**2


## Example number 1.12, Page number 13¶

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=7500;   #volume of cinema hall(m^3)
T=1.5;    #The reverberation time of the cinema hall(sec)

#Calculation
TaS=(0.167*V)/(T);     #The total absorbtion in the hall(sabine m^2)

#Result
print "The total absorbtion in the hall is",TaS,"sabine m^2"

The total absorbtion in the hall is 835.0 sabine m^2


## Example number 1.13, Page number 13¶

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

#Variable declaration
V=12500;    #volume of hall(m^3)
T1=1.5;     #The reverberation time of the hall(sec)
a2S2=200;   #The number of cushioned chairs are additionally placed in the hall(sabine-m^2)

#Calculation
Ta1S1=(0.167*V)/T1;    #The reverberation time before placed cushioned chairs(sabine m^2)
T2=(0.167*V)/(Ta1S1+a2S2);    #The new reverberation time after placing the cushioned chairs(sec)

#Result
print "The new reverberation time after placing the cushioned chairs is",round(T2,4),"sec"

The new reverberation time after placing the cushioned chairs is 1.3115 sec


## Example number 1.14, Page number 14¶

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

#Variable declaration
V=475;    #volume of hall(m^3)
a1=0.025;    #absorbtion coefficient for wall(O.W.U)
a2=0.02;     #absorbtion coefficient for the ceiling(O.W.U)
a3=0.55;     #absorbtion coefficient for the floor(O.W.U)
S1=200;    #The wall area of the room(m^2)
S2=100;    #The floor area of the room(m^2)
S3=100;    #The ceiling area of the room(m^2)

#Calculation
TaS=((a1*S1)+(a2*S2)+(a3*S3));   #The average absorbtion coefficient(O.W.U-m^2)
T=((0.167*V)/TaS);    #The reverberation time(sec)

#Result
print "The reverberation time for the hall is",round(T,4),"sec"

The reverberation time for the hall is 1.2794 sec


## Example number 1.15, Page number 14¶

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=2265;    #volume of hall(m^3)
Ta1S1=94.85;   #The total absorbtion coefficient(m^2)

#Calculation
T1=((0.167*V)/Ta1S1);    #The reverberation time in the hall without audience(sec)
Ta2S2=2*Ta1S1;   #The new absorbtion coefficient(m^2)
T2=((0.167*V)/Ta2S2);    #The reverberation time in the hall with audience(sec)

#Result
print "The reverberation time in the hall without audience is",round(T1,4),"sec"
print "The reverberation time in the hall with audience is",round(T2,5),"sec"
print "Thus,the reverberation reduces to half of its initial value when the audience fill the hall"

The reverberation time in the hall without audience is 3.9879 sec
The reverberation time in the hall with audience is 1.99396 sec
Thus,the reverberation reduces to half of its initial value when the audience fill the hall


## Example number 1.16, Page number 14¶

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=120000;   #Volume of the hall(m^3)
T=1.55;    #The reverberation time(sec)
S=26500;   #The total absorbing surface(m^2)

#Calculation
TaS=(0.167*V)/T;   #The average absorbtion coefficient(sabine-m^2)
a=(TaS/S);    #The average absorbing power of the surface(sabine)

#Result
print "The average absorbing power of the surface is",round(a,5),"sabine"

The average absorbing power of the surface is 0.48789 sabine