Hi Could someone please explain how to do this problem as I am unsure how to go about it... a trombone played fortissimo in the lower part of its range, around C3 (131Hz), has a sound level of about 100dB at a distance of 3m. A violin played fortissimo in the lower part of its range, around C4 (262Hz), has a sound level of about 80dB at the same distance. How many violins would need to play together to reach the same loudness level (in phons) as the trombone? eek..all I know is that I have to use the fletcher-munson graph but no idea how to actually interpret it!! Also...two harmonically rich notes are sounded together, one at a frequency of 294Hz and the other a perfect forth above this. it asks for the freq. of that note is-i calculated 392Hz but then it asks-at what frequencies are the first two shared harmonics?--what do i do? the other one asks-identifying the note at 294Hz as D4, what musical notes correspond to these shared harmonics?--how do i go about this one? Thanks
1) Find the loudness of the trombone in phons. On the equal loudness curves graph, go up to the 100dB and across to 131Hz. See where this lies relative to the equal loudness contours (it will be close to 100 phon line). 2) Follow that equal-loudness contour across to 262Hz, and see how many dB is needed to match it. Now you have your target sound level in decibels. 3) Figure out how many violins would produce that dB level. Can't help you with that one... you might get a faster response in the Arts and Culture forum.
Thanks Pete..but does all along EACH curve represnt the #in phons. So I went up to 100dB and indeed as I go across to 131 it lies within the 100phon curve, then I follow it along and I end up at around 95dB...is this correct? Then I looked atthe graph of how many = sound sources must play and it only goes up to 10dB...I don't know what to do after that...also as it tells me to work this out in phons..looking at the fletcher-munson curve is just the same as working it out in phons right?
That sounds about right Please Register or Log in to view the hidden image!, depending on the particular dataset (there are a few) of your graph, and how good the resolution is. For this one, I get maybe 97 or 98. But it's pretty rough. Please Register or Log in to view the hidden image! If that graph is what I think, then it says that 3 sources is 4.8dB and 10 sources in 10dB, right? What this means is that multiplying the power of any sound (whether it's an instrument, a quartet, an orchestra, or whatever) by three will increase its sound level by 4.8dB. Multiplying the power by 10 will increase its sound level by 10dB. Now. We know that at our target range one violin produces 80dB. We need to know how many violins would make 95dB, but our chart doesn't tell us. So we need to cheat a little. How many violins would make 90dB (a 10dB boost)? Put those violins in a box, and call it a superviolin - one superviolin makes 90dB. (crappy analogy, I know Please Register or Log in to view the hidden image!) How many superviolins make 95dB?
Hi there yep thats the right chart.. Well in order to increase it by 10dB 10 violins would have to play right? hence 10 violins=one superviolin Please Register or Log in to view the hidden image! but then you say how many superviolins would make 95dB..this is an extra 5dB....hmmm I am unsure what to do now...sorry Please Register or Log in to view the hidden image! physics_06er
Hi there its between 3-4 so rounding upwards it would be 4 hence 10 violins plus 4 violins =14 violins? is this correct?
Hi there your self (and welcome). I am not normally this stupid, but just now I can't help myself resist: 10dB is one Bell - so you need a bell to increase 10dB Please Register or Log in to view the hidden image!
it must be 60 then right as the 10 violins=a super violin=10dB therefore if we need a 5 more dB and each db is a superviolin then it must be 10x5=50+10=60?...right?
No, each dB is not a superviolin. You have a graph that looks something like this? Please Register or Log in to view the hidden image! Going across the graph is the number of sound sources (superviolins). Going down the graph is how many more dB that number of sound sources makes than a single sound source. For example, 1 sound source is zero dB on the graph. That means that one superviolin makes zero more dB than a single superviolin (obviously!) So how many superviolins make 5 more dB than a single superviolin?
between 3-4 superviolins would be needed!!!---..I came across a site that provides a formula.. http://www.sengpielaudio.com/calculator-spl.htm Formulas: Δ L = 10 log n or n = 10Δ L / 10 using this formula I got around 51.1(52) sources---I have to hand in my assignment tomorrow so I'm hoping this is right--however I will keep looking at the "superviolin" analogy to see if I can understand it... Thanks for all your help most appreciated! physics_06er
All correct, except the 51.1 bit... ΔL = 15 right? 10<sup>ΔL/10</sup> = 10<sup>1.5</sup> = 31.6 So, I make it 32 sources (3.2 superviolins!) for a 15dB boost. Glad to help!
I was taking ΔL=19, cos from the graph you posted above 97dB looked more accurate than 95..but I "think" ive got the superviolin analogy now...in the beg. you said that 10 violins=10dB boost (calling it a superviolin)...then for the 2nd part you said how many superviolins needed for a 5dB boost (this was around 3.2)....meaning 10x3.2=32normal violins (as each superviolin has 10 violins)..have i understood this correctly?? yay if i have!! Please Register or Log in to view the hidden image!
A harmonic is a small integral multiple of the fundamental frequency of vibration. So you have to find one small number you can multiply the first frequency by and another you can multiply the second frequency by so they result in the same (harmonic) frequency. For example if you have a G string vibrating at 24hz and a D string a fourth above it at 36 hz, their lowest common harmonic is D an octave up, 72hz = 3*24 = 2*36. The numbers in your problem are not as easy to work with by inspection as these, but I think you can now see the technique involved. You can usually solve problems by inspection or trial and error when you know the answers have got to be small integers. If you want to find what note corresponds to a specific frequency, use the scientific chromatic scale. Every half step is an interval of 2^(1/12) and reference A = 440hz.
