Decibels

Hi fellas

I have my final exam for the semester tomorrow. It's multiple choice so who cares right but the thing is I don't understand this infernal logarithmic scale sound intensity/decibels THING!?

MATHS

eg.

  Quote

if a violin has twice the sound intensity of a viola, how many decibels louder is it?

huh

I thought that if something is 100 times as loud as something else it is 20dB louder (100 divided by 10 times 2, yes?)

So then the viola thing would be .4dB

I'm sorry for pooing all over the music forum with this but if someone could make sense of this I would appreciate.

I love you

Wouldn't it be like in your course notes or something ... ?

Thanks mesh. I can't be arsed

  On 6/15/2010 at 1:51 PM, Mesh Gear Fox said:

  On 6/15/2010 at 12:00 PM, verticalhold said:

Hi fellas

 

I have my final exam for the semester tomorrow. It's multiple choice so who cares right but the thing is I don't understand this infernal logarithmic scale sound intensity/decibels THING!?

MATHS

 

eg.

  Quote

if a violin has twice the sound intensity of a viola, how many decibels louder is it?

 

huh

 

I thought that if something is 100 times as loud as something else it is 20dB louder (100 divided by 10 times 2, yes?)

 

So then the viola thing would be .4dB

 

 

 

I'm sorry for pooing all over the music forum with this but if someone could make sense of this I would appreciate.

 

I love you

6db increase = twice as loud, yes?

sound intensity is a measure of power/area. to use an example from my electronics courses that may be illustrative, the 3 dB frequency of a resonant circuit is the frequency at which the original power delivered to the circuit drops by half. thus, a 3 dB increase would mean double the power. could be wrong though; my early morning math skills are subject to change wildly from day to day.

if the question had asked for sound pressure, i think the answer would be 6 dB. once again, i'm not 100% on this

the crux of this question is that dB is only used as a relative measurement for any two quantities. there is a difference between measuring two powers in dB, like is asked in the original question, and measuring sound pressures in dB.

as for answering the other question you had posed in the OP, i'm not sure how the human ear perceives things as being incrementally louder; i don't know if it's the sound intensity or the sound pressure that ultimately affects how we perceive loudness.

but anyways, if the sound intensity were 100 times greater, the increase in dB would be as follows:

P_original = 1 (doesn't matter; it's only being used as a reference)

P_new = 100*P_original = 100*1 = 100

dB = 10 * log10(P_new/P_original) = 10 * log10(100/1) = 10 * log10(100) = 10 *2 = 20 dB (sound intensity)

This is how i got the 3 dB, since 10*log10(2) = 10 * 0.301 = 3.01 dB.

if the sound pressure were 100 times greater, formula needs changing

dB = 10 * log10(P_new^2/P_original^2) = 20 * log10(P_new/P_original) by law of logarithms

dB (sound pressure) = 20 * log10(100) = 40 dB (sound pressure)

Thanks man. I'm just going to have to let this go

it's not that difficult if you had someone explaining it to you personally

it's quite easy to grasp

what happens is that it is not a linear increase, it is logaritmic!

3dB is a doubling of power. 6dB is a doubling of amplitude. 10dB is a doubling of perceptive loudness.

It depends on how you're measuring it.

  On 6/15/2010 at 8:41 PM, Braintree said:

3dB is a doubling of power. 6dB is a doubling of amplitude. 10dB is a doubling of perceptive loudness.

 

It depends on how you're measuring it.

and you condensed my ramblings into about 30 words, bravo. i'm sure this would have been helpful in the first place

Cheers

Hah, shit wasn't even on the test! Thanks dudes, I understand it now after the fact.

let me see if i can give you a quick and dirty description of why. power is a measure of the amount of energy expended over a certain length of time. in many things in nature, sound waves included, the energy given off or radiated by a physical process is proportional to the amplitude of oscillation squared. this should make since because the energy you can elicit out of something has to be dependent of the amplitude/"strengeth" of the wave or the force.

for instance, the power given off by a resistor supplied with a certain voltage is proportional to that voltage squared (see a textbook for derivation). so plugging the into the formula. you would be putting in something like

P = 10*log10(x^2)

but by one of the laws of logarithms, that exponent can be moved to the front so

P = 20*log10(x).

This is why the amplitude dB measurement is twice as large as the power dB measurement.

end rant