Sound pressure level magnitude question.

[soundguy]

Hey all,

I've got an audio related question for you guys/gals:

I understand the logarithmic relationship to SPL, but would someone help me out with a simple question and post a formula as to how you arrive at an answer? Assuming a start value of 150 decibels, what pressure level would represent a magnitude of 1000 times increase over 150dB?

-As a side note, cool forum! Everything from mathematics to religion and alien abduction; you don't find that often! I'm sure I'll be spending too much free time reading threads in the future.

Thanks!

 

[rbj]

Hey all,

I've got an audio related question for you guys/gals:

I understand the logarithmic relationship to SPL, but would someone help me out with a simple question and post a formula as to how you arrive at an answer? Assuming a start value of 150 decibels, what pressure level would represent a magnitude of 1000 times increase over 150dB?

do you mean, what dB level for 1000 times more sound pressure? or what is the pressure level for 150,000 dB (i think 150,000 dB SPL will liquify everything.)

-As a side note, cool forum! Everything from mathematics to religion and alien abduction; you don't find that often! I'm sure I'll be spending too much free time reading threads in the future.
Thanks!

i don't deal with the alien abduction and haven't seen any religion here.

but i don't do all of the forums.

 

[soundguy]

do you mean, what dB level for 1000 times more sound pressure? or what is the pressure level for 150,000 dB (i think 150,000 dB SPL will liquify everything.)

Right on the first part...what sound pressure level would be 1000 times more spl than 150db.

i don't deal with the alien abduction and haven't seen any religion here.

but i don't do all of the forums

It's down in the Lounge and Philosophy sections.

 

[soundguy]

No one?

 

[rbj]

Right on the first part...what sound pressure level would be 1000 times more spl than 150db.

well, think of pressure like voltage and particle velocity like current. for example, a spherically expanding sound wave will obey the inverse-square law as far as power (more specifically, intensity, which is power per unit area) so the power or intensity is reduced by a factor of 4 (or and additive gain of -6.02 dB) every time the distance from the point source is double. also, for a sound wave front, the r.m.s. pressure times the r.m.s. particle velocity (the component of the particle velocity that is in-phase with the pressure wave) multiply to be intensity, and it also turns out that both are 1/r. so to reduce the magnitude of the pressure wave by a factor of 1000, i would have to increase my distance by a factor of 1000, which means i double it about 10 times (2¹⁰ = 1024) so that would be about 60 dB. (in fact it would be exactly 60 dB if you look at the exact definition of dB.) so i guess your answer is 210 dB which is so friggin' loud, only a martyr or a masochist would be willing to be subjected to it. 0 dB is roughly the threshold of hearing and 130 is roughly the threshold of pain and 150 dB is louder than anything i would ever want to hear.