How Do Decibel Levels Combine in Different Scenarios?

[nokia8650]

1. What is the total sound pressure levels of two identical tones, each 88db SPL, when added together?

For this question, using the equation dB SPL = 20log(P/2*10^-5), I found the value of P where dB SPL = 88, then doubled this value, then fed it back into the equation, to obtain a value of 94 db SPL. Is this correct?

2. If A is 20dB above B and B is 40dB above C, how many decibels is A above C?
I was struggling with this question - does anyone have any advice on how to tackle it?

 

[ideasrule]

1. What is the total sound pressure levels of two identical tones, each 88db SPL, when added together?
For this question, using the equation dB SPL = 20log(P/2*10^-5), I found the value of P where dB SPL = 88, then doubled this value, then fed it back into the equation, to obtain a value of 94 db SPL. Is this correct?

Yes. A less tedious way to do it would be to realize that log(2x)=log(x)+log(2), so dB SPL increases by 20*log(2).

2. If A is 20dB above B and B is 40dB above C, how many decibels is A above C?
I was struggling with this question - does anyone have any advice on how to tackle it?

Why would it not be 60? If you need to convince yourself, 20dB corresponds to a factor of 100, 40dB to a factor of 10,000. A is 100 times louder than B and B is 10,000 times louder than C, so A should be 10^6 times louder than C. That's 60 dB.

 

[nokia8650]

Ahh yes I see, thank you! However, does 20dB not correspond to a factor of 10, and 40dB to a factor of 100, given the fact it is dB SPL, and hence 20logx as opposed to 10logx?

Also, the next part of the question asks - if the sound pressure of D is four times that of E, by how many decibels do they differ? For this, would one simply find 20log4?

Thanks again

 

[ideasrule]

Ahh yes I see, thank you! However, does 20dB not correspond to a factor of 10, and 40dB to a factor of 100, given the fact it is dB SPL, and hence 20logx as opposed to 10logx?

Oops. You're completely right--it should be a factor of 10, not 20. Sorry about that.

Also, the next part of the question asks - if the sound pressure of D is four times that of E, by how many decibels do they differ? For this, would one simply find 20log4?

Yes.

 

[rwisz]

1. The total sound pressure level of two identical tones, each 88db SPL, when added together is 94 dB SPL. This is correct. When adding decibel levels, we use the formula dB(total) = 10log(10^(dB1/10) + 10^(dB2/10)). In this case, 10^(88/10) + 10^(88/10) = 10^(94/10) which results in a value of 94 dB SPL.

2. To determine the decibel difference between A and C, we first need to find the decibel difference between A and B, and then between B and C. We can use the formula dB(A-B) = dB(A) - dB(B). So, dB(A-B) = 20dB - 40dB = -20dB. Similarly, dB(B-C) = 40dB - 0dB = 40dB.

To find the decibel difference between A and C, we add the decibel differences between A and B, and B and C. So, dB(A-C) = dB(A-B) + dB(B-C) = -20dB + 40dB = 20dB.

Therefore, A is 20dB above C.