# Decibel levels homework

1. Nov 18, 2006

### gh0st

Question

15. (a) Show that the difference in decibel levels, B1 and B2, of a sound source is related to the ratio of its distances, r1 and r2, from the receivers by

B2 - B1 = 20 log (r1/r2)

(b) A speaker is placed between two observers who are 110 m apart, along the line connecting them. If one observer records an intensity level of 80 dB, how far is the speaker from each observer ?

Answer given by lecturer : [ 10 m and 100 m ]

====================================================

Before i start, i would like to apologize for the messy post as i have no idea how to type out the actual symbols, therefore i'm only using those basic ones on my keyboard ..

Okay, this is my problem ... I managed to solve 15(a) but i'm stuck at 15(b)

====================================================

According to 15(b), i came up with this diagram :

My worksteps

Formulas used :

i. Intensity Level in Decibels, B = 10 log ( I / Io ) dB ... ( Io is intensity reference, 1.00 x 10^-12 Wm^-2 )

ii. Intensity , I = Power / Area ... ( Area is 4*pi*r^2 )

iii. Assumed that Observer 1 was the person who recorded 80dB mentioned. Therefore :

80dB = 10 log ( I / Io ) dB

Intensity 1 = [ anti-log ( 80/10) ]*[Io]
= ( 1 x 10^-8 )*(1x10^-12)
= 1 x 10^-4 Wm^-2

iv. Used Intensity formula :

I = P/A
I = P/4*pi*r^2
1 x 10^-4 = P/4*pi*r^2

P = ( 1 x 10^-4 )*4*pi*r^-2

v. Okay, so P, Power is not given, so i thought of deriving it from Observer 2, using the Intensity formula ...

Intensity 2 = P/4*pi*r^-2 , however this r is ( 110-r ) , as it's the distance between speaker and obersver 2, as shown in the diagram ..

P = Intesity2*4*pi*[(110-r)^-2]

vi. Since the sound is coming from 1 speaker therefore the value for P should be the same ...

P = ( 1 x 10^-4 )*4*pi*r^-2 and P = Intesity2*4*pi*[(110-r)^-2]

vii. I concluded that

( 1 x 10^-4 )*4*pi*r^-2 = Intesity2*4*pi*[(110-r)^-2][/b]

viii. However, the problem is there are 2 unknown variables here ... Intensity 2 and r ( which is sought by the question ... ) And i got stuck here ... Tried many ways in substituting either r or intensity but i got back the same equation .... Also, the reason i posted along 15(a) is because i was wondering if (b) is related to (a) , but i can't find any connection ..

===================================================