Public mathematics with help from Jo.

[apiphile]

5. Calculate the pressure amplitudes for SPL readings of 26dB and 20dB. How are the two pressure amplitudes related?

dB = 20log (input/ref)

Part 1:

26 / 20 = 1.3

log(ref) = -4.698970

1.3 + -4.698970 = -3.39897

10^-3.39897 = 3.990524
3.990524 N/m^2 which is basically 4 N/m^2

which doesn't make any sense at all because 56dB came out as less Newtons per

Comments

[kalorlo]

I got the answer for part 1 to be 0.00039905246698. But I don't know what units go where. Are you given the log(ref) as a standard?

[apiphile]

I think I am clearly doing something assbackward but I don't know what. And yes, the log(ref) is based on the universally accepted threshold of hearing, which is 20μN/m^2.

[kalorlo]

I just plugged the numbers in to the scientific calculator at http://web2.0calc.com/. You seem to be losing decimal places. I mean, what I've written is the same as 3.993x10^-4. Is your calculator saying that? Would explain your tweet about those numbers both coming out the same.

[kalorlo]

Whoops, I mean 3.9905x10^-4... The same number as I said above, but you count what place the 3 is after the decimal point and write it as an exponent so you don't have to write out all the zeroes.

[apiphile]

It's been being weird, I get some which are consistent and make sense and some which are deranged and I don't know if I'm haemorrhaging decimal places or what.

[kalorlo]

Yeah, because 10^-1.198970 and 10^-0.19897 will give the same numbers, but one is 0.06324555383482 and the other is 0.63245553834815.

[apiphile]

I figured that one out eventually! I just need to know why 20dB and 26dB came out ASTRONIMICALLY HIGHER than 50dB and 90dB and so on... it's meant to be the other way around!

[kalorlo]

Ok, I get that 50dB should be 0.00632455538348. Which is a higher pressure than the number for 26dB.

[apiphile]

Yeah I got ... what the hell did I get for 26dB?

[kalorlo]

Yeah, that's where the decimals went AWOL. Did your calculator start showing EXP-4 or something as well as the number? Because with that many zeroes, most of them will switch to writing it that way.

[apiphile]

Aaaaa. It said e4, yes.

[kalorlo]

Success! You got the right answer all along :)

[kalorlo]

Ooh, they actually write it as 3.9905E-04 usually. It's all coming back!

[apiphile]

GRAWR HOW UNHELPFUL OF THEM.

[kalorlo]

It does have a reason, but yeah. Should be much more obvious than it is.

(It's in case you have a number like 0.0000000000067589484984. The calculator can only show some of the digits, so that would show up as zero if it didn't use the other notation. Same for really big numbers).

[flutterbyeaten]

I"m pleased that someone helped with this... I spotted the mistake at the first reading, but i was in work today!