- #1
Kingsley
- 9
- 0
QUESTION 1
A guitar string is 0.70m long and is tuned to play an E above middle C (330 Hz). How far from the end of this string must a finger be placed to play A above middle C (440Hz)
[tex]\lambda[/tex] = 2L/n
[tex]\lambda[/tex] = v/f
v = [tex]\lambda[/tex] x f
[tex]\lambda[/tex] = 2L/n
[tex]\lambda[/tex] = 2(0.70m)/1
[tex]\lambda[/tex] = 1.4m
v = [tex]\lambda[/tex] x f
v = (1.4m)(330Hz)
v = 462m/s
[tex]\lambda[/tex] = v/f
[tex]\lambda[/tex] = 462m/s/440Hz
[tex]\lambda[/tex] = 1.05
[tex]\lambda[/tex] = 2L/n
[tex]\lambda[/tex] = L/2
[tex]\lambda[/tex] = 1.05m/2
[tex]\lambda[/tex] = 0.525m
that is the right math i don't know what to add to find how far to place your finger though, help/explanation would be appreciated.
QUESTION 2
If you were to build a pipe organ with closed tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of pipes required?
[tex]\lambda[/tex] = 2L/n
[tex]\lambda[/tex] = v/f
v = [tex]\lambda[/tex] x f
[tex]\lambda[/tex] = 2L/n <<< SIDE NOTE: what's the difference between
[tex]\lambda[/tex] = 4L/2n - 1 these two equations?
v/f = [tex]\lambda[/tex]
[tex]\lambda[/tex] = 340m/s/20Hz
[tex]\lambda[/tex] = 17m
[tex]\lambda[/tex] = 340m/s/20000Hz
[tex]\lambda[/tex] = 0.017m
i have no idea what to do after this any help would be appreicated. thanks in advance.
Homework Statement
A guitar string is 0.70m long and is tuned to play an E above middle C (330 Hz). How far from the end of this string must a finger be placed to play A above middle C (440Hz)
Homework Equations
[tex]\lambda[/tex] = 2L/n
[tex]\lambda[/tex] = v/f
v = [tex]\lambda[/tex] x f
The Attempt at a Solution
[tex]\lambda[/tex] = 2L/n
[tex]\lambda[/tex] = 2(0.70m)/1
[tex]\lambda[/tex] = 1.4m
v = [tex]\lambda[/tex] x f
v = (1.4m)(330Hz)
v = 462m/s
[tex]\lambda[/tex] = v/f
[tex]\lambda[/tex] = 462m/s/440Hz
[tex]\lambda[/tex] = 1.05
[tex]\lambda[/tex] = 2L/n
[tex]\lambda[/tex] = L/2
[tex]\lambda[/tex] = 1.05m/2
[tex]\lambda[/tex] = 0.525m
that is the right math i don't know what to add to find how far to place your finger though, help/explanation would be appreciated.
QUESTION 2
Homework Statement
If you were to build a pipe organ with closed tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of pipes required?
Homework Equations
[tex]\lambda[/tex] = 2L/n
[tex]\lambda[/tex] = v/f
v = [tex]\lambda[/tex] x f
[tex]\lambda[/tex] = 2L/n <<< SIDE NOTE: what's the difference between
[tex]\lambda[/tex] = 4L/2n - 1 these two equations?
The Attempt at a Solution
v/f = [tex]\lambda[/tex]
[tex]\lambda[/tex] = 340m/s/20Hz
[tex]\lambda[/tex] = 17m
[tex]\lambda[/tex] = 340m/s/20000Hz
[tex]\lambda[/tex] = 0.017m
i have no idea what to do after this any help would be appreicated. thanks in advance.