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.