# What are the Decibel Levels of Two Combined 70 dB Sound Sources?

• MathematicalPhysicist
In summary: Originally posted by MathNerd Notice that in my post I had the following4*I = k (C*2)^2notice that the C*2 is all squaredSo, k (C*2)^2 = k C^2 2^2 = 4k C^2So, 4*I = 4k C^2therefore your expression is equivalent to mine.In summary, we discussed two questions from the text "Music and Mathematics" by Dave Benson. The first question was about the decibel representation of a doubling of amplitude and the second question was a multiple choice question about the loudness of two 70 dB sound sources. We provided a formula for calculating decibels and
MathematicalPhysicist
Gold Member
im reading the text of dave benson about music and maths and i have 2 questions from the text which i need an answer to.
1. power intensity is proportional to the square of the amplitude. how many decibles represent a doubling of the amplitude of a signal?
(my answer is 4 but I am not sure).
2. (multiple choices) two independents 70 dB sound sources are heard together. how loud is the resultant sound to the nearest dB?

a. 140 dB
b. 76 dB
c. 73 dB
d. 70 dB
e. none of above

now I am stuck at it because i think it is either a or d.

thanks for any help.

Originally posted by loop quantum gravity
im reading the text of dave benson about music and maths and i have 2 questions from the text which i need an answer to.
1. power intensity is proportional to the square of the amplitude. how many decibles represent a doubling of the amplitude of a signal?
(my answer is 4 but I am not sure).
2. (multiple choices) two independents 70 dB sound sources are heard together. how loud is the resultant sound to the nearest dB?

a. 140 dB
b. 76 dB
c. 73 dB
d. 70 dB
e. none of above

now I am stuck at it because i think it is either a or d.

thanks for any help.
I'm not sure about the first question but I will happily answer the second. The formula for decibles is

B = 10*log(I/A)

where B is the number of decibles, A is the reference level which is 10^-12 watts per metre^2 and I is the intensity of the sound. Now a 70dB source has an intensity as follows

70 = 10*log(I/A)
10^7 = I/A
I = A 10^7

there are two 70dB sources in total so the above intensity will be doubled. Therefore the total intensity is

I = 2*10^7 A

putting this back into the decible formula

B = 10*log(I/A)
B = 10*log(2*10^7 A / A)
B = 10*[log(2)+log(10^7)]
B = 10*[log(2)+7]
B &asymp; 73.0103dB

So (c) would be the correct answer!

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thanks, surprsingly i haven't met this formula in the text.

Originally posted by loop quantum gravity
thanks, surprsingly i haven't met this formula in the text.
It is quite stupid of the author then to set problems without teaching the machinary to solve them!

indeed.
you can find the text I am talking about in here http://www.math.uga.edu/~djb/html/music-hq.pdf
the problems are at page number 11.

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I haven't taken a look at the book but I will take a shot at the first question you asked. I'm not quite sure what "power intensity" is but I will make the assumption that power intensity = intensity = I. The question is restated below

"power intensity is proportional to the square of the amplitude. how many decibles represent a doubling of the amplitude of a signal?
(my answer is 4 but I am not sure)."

therefore I = k C^2, where C is the amplitude and k is the constant of proportionality.

it is easily shown that 4*I = k (C*2)^2, therefore doubling the amplitude quadruples the intensity. So using the formula I used in my last post

B = 10*log(I/A)

now doubling the amplitude quadruples the intensity so

B'= 10*log(4*I/A)
B'= 10*log(4)+10*log(I/A)
B'= 10*log(4)+B

therefore if my assumption is correct i.e. power intensity is just another word for intensity, then the number of decibles corrosponding to a doubling of the amplitude is 10*log(4)&asymp;6.0206dB.

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Originally posted by MathNerd
I haven't taken a look at the book but I will take a shot at the first question you asked. I'm not quite sure how amplitude fits in with dB but I will make the assumption that power intensity = intensity = I. The question is restated below

"power intensity is proportional to the square of the amplitude. how many decibles represent a doubling of the amplitude of a signal?
(my answer is 4 but I am not sure)."

therefore I = k C^2, where C is the amplitude and k is the constant of proportionality.

it is easily shown that 4*I = k (C*2)^2, therefore doubling the amplitude quadruples the
tell me if I am wrong but when you multiply I=k*C^2 by 4 it should be 4I=4kC^2.

Originally posted by loop quantum gravity
tell me if I am wrong but when you multiply I=k*C^2 by 4 it should be 4I=4kC^2.
Notice that in my post I had the following
4*I = k (C*2)^2

notice that the C*2 is all squared

So, k (C*2)^2 = k C^2 2^2 = 4k C^2
So, 4*I = 4k C^2

therefore your expression is equivalent to mine.

## 1. What is sound and how is it produced?

Sound is a form of energy that is produced when an object vibrates. When an object vibrates, it creates sound waves that travel through the air and reach our ears. Our ears then interpret these sound waves and allow us to hear different sounds.

## 2. How does sound travel through different mediums?

Sound travels through different mediums, such as air, water, and solids, by causing the particles in the medium to vibrate. These vibrations then pass from one particle to the next, creating a chain reaction and allowing sound to travel through the medium. The speed of sound varies depending on the medium it is traveling through.

## 3. What is the difference between pitch and volume of sound?

Pitch refers to how high or low a sound is, and it is determined by the frequency of the sound wave. The higher the frequency, the higher the pitch. Volume, on the other hand, refers to the loudness or softness of a sound, and it is determined by the amplitude of the sound wave. The larger the amplitude, the louder the sound will be.

## 4. How does sound affect our daily lives?

Sound plays a significant role in our daily lives. We use sound to communicate with others, to enjoy music and other forms of entertainment, and to be aware of our surroundings. It also helps us to detect potential dangers, such as loud noises indicating a possible threat.

## 5. Can sound travel through a vacuum?

No, sound cannot travel through a vacuum. A vacuum is a space without any particles, so there is nothing for the sound waves to vibrate and travel through. This is why sound cannot travel through outer space, which is mostly a vacuum.

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