Page 2 of 3
Re: Sounds of Music C
Posted: October 16th, 2019, 11:53 am
by gz839918
Giantpants wrote: ↑October 16th, 2019, 11:25 am
gz839918 wrote: ↑October 16th, 2019, 5:46 am
Alice and Bob are playing a duet. Alice is supposed to play a note at 110.0 Hz and Bob is supposed to play a note at 164.8 Hz, but Bob accidentally plays his note 50 cents sharper than he is supposed to play it.
(a) What frequency does Bob actually play?
(b) If the interval between the notes is supposed to be a perfect fifth, Alice and Bob are playing most closely in what system of temperament? (
A) Pythagorean (
B) 12-tone equal (
C) Just intonation (aka 5-prime) (
D) All of these could be correct
(a) 113.2 Hz
(b) I’m not so sure, but I think it might be D. all of the above, since the frequency ratio is always 3:2?
For part (a),
Bob wants to play a note at 164.8 hertz. If it were Alice who played 50 cents higher, then 113.2 Hz would be correct, but it is Bob whose note is too sharp. Maybe it was just misreading the question, but I'm guessing you have a pretty solid understanding of the math behind this.
For (b),
if Bob had intended to play 165.0 Hz, then the ratio would be 3/2. But because the 8 in the tens place is a significant figure, we know that he really means to play 164.8 and not 165.0 Hz. Not every temperament has perfect fifths in ratio of 3/2, so try eliminating the ones that do require 3/2...
Re: Sounds of Music C
Posted: October 16th, 2019, 1:47 pm
by Giantpants
gz839918 wrote: ↑October 16th, 2019, 11:53 am
For part (a),
Bob wants to play a note at 164.8 hertz. If it were Alice who played 50 cents higher, then 113.2 Hz would be correct, but it is Bob whose note is too sharp. Maybe it was just misreading the question, but I'm guessing you have a pretty solid understanding of the math behind this.
For (b),
if Bob had intended to play 165.0 Hz, then the ratio would be 3/2. But because the 8 in the tens place is a significant figure, we know that he really means to play 164.8 and not 165.0 Hz. Not every temperament has perfect fifths in ratio of 3/2, so try eliminating the ones that do require 3/2...
Oops lol, so that means (a) is actually
169.6 Hz
As for (b),
looking closer I see the notes are 700 cents apart, as opposed to justly tuned 702 cents, so I’m gonna go with 12 tone equal tempered?
Re: Sounds of Music C
Posted: October 16th, 2019, 3:57 pm
by gz839918
Giantpants wrote: ↑October 16th, 2019, 1:47 pm
gz839918 wrote: ↑October 16th, 2019, 11:53 am
For part (a),
Bob wants to play a note at 164.8 hertz. If it were Alice who played 50 cents higher, then 113.2 Hz would be correct, but it is Bob whose note is too sharp. Maybe it was just misreading the question, but I'm guessing you have a pretty solid understanding of the math behind this.
For (b),
if Bob had intended to play 165.0 Hz, then the ratio would be 3/2. But because the 8 in the tens place is a significant figure, we know that he really means to play 164.8 and not 165.0 Hz. Not every temperament has perfect fifths in ratio of 3/2, so try eliminating the ones that do require 3/2...
Oops lol, so that means (a) is actually
169.6 Hz
As for (b),
looking closer I see the notes are 700 cents apart, as opposed to justly tuned 702 cents, so I’m gonna go with 12 tone equal tempered?
Nicely done! Your turn!
Re: Sounds of Music C
Posted: October 17th, 2019, 6:47 am
by Giantpants
You’re at a Fall Out Boy concert and are 7 meters from a speaker. You determine that the music is 90 dB where you are, and it’s too loud. So, you decide to go further from the speaker until it’s only 60 dB. How far are you from the stage now?
Re: Sounds of Music C
Posted: October 17th, 2019, 7:55 am
by wec01
Giantpants wrote: ↑October 17th, 2019, 6:47 am
You’re at a Fall Out Boy concert and are 7 meters from a speaker. You determine that the music is 90 dB where you are, and it’s too loud. So, you decide to go further from the speaker until it’s only 60 dB. How far are you from the stage now?
A decrease of 30 dB corresponds to a decrease in sound intensity by a factor of 1000 which is proportional to distance squared. So the distance is 7 m * sqrt(1000) = 221 m
Re: Sounds of Music C
Posted: October 17th, 2019, 9:57 am
by Giantpants
wec01 wrote: ↑October 17th, 2019, 7:55 am
A decrease of 30 dB corresponds to a decrease in sound intensity by a factor of 1000 which is proportional to distance squared. So the distance is 7 m * sqrt(1000) = 221 m
Yep, I did it the same way, I
found the acoustic power using the 90 dB, which turned out to be 0.6157 W, which I plugged into r^2 = P/(4pi * intensity), using the intensity of 60 dB for I. Same idea, just not in one step lol.
Your turn!
Re: Sounds of Music C
Posted: October 18th, 2019, 11:59 pm
by wec01
https://musescore.com/static/musescore/ ... 1531731515
1. What key is this passage in?
2. Does this passage have a simple or compound meter?
3. What is the interval between the last two notes of the 6th measure of the treble part?
Re: Sounds of Music C
Posted: October 20th, 2019, 2:27 pm
by linzhiyan
1. b minor
2. Compound
3. perfect fourth
Ahahaha music theory...
Re: Sounds of Music C
Posted: October 20th, 2019, 3:01 pm
by wec01
linzhiyan wrote: ↑October 20th, 2019, 2:27 pm
1. b minor
2. Compound
3. perfect fourth
Ahahaha music theory...
Yup, except
for number 3 it’s a minor 3rd. I think you may have been looking at a different measure.
Your turn!
Re: Sounds of Music C
Posted: October 21st, 2019, 2:32 pm
by linzhiyan
1. An airplane is flying at a height of 11,000 m. Given that the temperature outside the airplane is -56.5ºC, what is the speed of sound outside the airplane?
2. Given the frequency of A3 is 250 Hz, what is the frequency of C4?
