jeremymacgregor87 Posted June 15, 2010 Share Posted June 15, 2010 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. 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 Link to comment Share on other sites More sharing options...
mcbpete Posted June 15, 2010 Share Posted June 15, 2010 Wouldn't it be like in your course notes or something ... ? Link to comment Share on other sites More sharing options...
jeremymacgregor87 Posted June 15, 2010 Author Share Posted June 15, 2010 Thanks mesh. I can't be arsed Link to comment Share on other sites More sharing options...
benc812 Posted June 15, 2010 Share Posted June 15, 2010 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. 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 Link to comment Share on other sites More sharing options...
benc812 Posted June 15, 2010 Share Posted June 15, 2010 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) Link to comment Share on other sites More sharing options...
jeremymacgregor87 Posted June 15, 2010 Author Share Posted June 15, 2010 Thanks man. I'm just going to have to let this go Link to comment Share on other sites More sharing options...
cruising for burgers Posted June 15, 2010 Share Posted June 15, 2010 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! Link to comment Share on other sites More sharing options...
Braintree Posted June 15, 2010 Share Posted June 15, 2010 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. Link to comment Share on other sites More sharing options...
benc812 Posted June 15, 2010 Share Posted June 15, 2010 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 Link to comment Share on other sites More sharing options...
Braintree Posted June 15, 2010 Share Posted June 15, 2010 Cheers Link to comment Share on other sites More sharing options...
jeremymacgregor87 Posted June 16, 2010 Author Share Posted June 16, 2010 Hah, shit wasn't even on the test! Thanks dudes, I understand it now after the fact. Link to comment Share on other sites More sharing options...
benc812 Posted June 16, 2010 Share Posted June 16, 2010 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 Link to comment Share on other sites More sharing options...
Recommended Posts
Archived
This topic is now archived and is closed to further replies.