Sounds Of Music C

[smayya337]

Here's my go: (Click to Show Hidden Text)

1) Longer bars will have a lower pitch. You can have a higher frequency by shortening the bar.
2) Making a bar thinner by carving material out from the bottom will lower the pitch.
3) Width has no effect on pitch as far as I know...

And as far as I know, you are correct!

[UTF-8 U+6211 U+662F]

Well, here's a bit about idiophones:
1) What does changing the length of a bar on an idiophone do to the bar's pitch?

2) What does changing the thickness of a bar on an idiophone do to the bar's pitch?

3) What does changing the width of a bar on an idiophone do to the bar's pitch?

Here's my go: (Click to Show Hidden Text)

1) Longer bars will have a lower pitch. You can have a higher frequency by shortening the bar.
2) Making a bar thinner by carving material out from the bottom will lower the pitch.
3) Width has no effect on pitch as far as I know...

To add onto this, I don't think all idiophones have bars

[mjcox2000]

Well, here's a bit about idiophones:
1) What does changing the length of a bar on an idiophone do to the bar's pitch?

2) What does changing the thickness of a bar on an idiophone do to the bar's pitch?

3) What does changing the width of a bar on an idiophone do to the bar's pitch?

Here's my go: (Click to Show Hidden Text)

1) Longer bars will have a lower pitch. You can have a higher frequency by shortening the bar.
2) Making a bar thinner by carving material out from the bottom will lower the pitch.
3) Width has no effect on pitch as far as I know...

To add onto this, I don't think all idiophones have bars

That’s true, but the general principle holds for all idiophones — i.e. a thinner or larger-diameter cymbal is lower while a thicker or smaller one is higher; on a kalimba, lower notes are longer or thinner; and so on.

[olivia.m19]

Ok here's my question:

1) What are cents and hertz? How are they related? Can they be converted (as in, can you answer how many cents are in 1 hz)? Why/why not?
2) Let's say I am tuning my violin. My A string is out of tune and has a frequency of 438 hz. How many cents is it off by?

[mjcox2000]

Ok here's my question:

1) What are cents and hertz? How are they related? Can they be converted (as in, can you answer how many cents are in 1 hz)? Why/why not?
2) Let's say I am tuning my violin. My A string is out of tune and has a frequency of 438 hz. How many cents is it off by?

1) Hertz is a measurement of cycles per second. Cents are a logarithmic measure of frequency difference, with 100 cents per semitone.
Cents can only be used as a measurement relative to some reference value, while Hertz can be relative or absolute. For example, I can have a 440Hz note (an absolute frequency), but the idea of a 100 cent note makes no sense. In terms of relative measurements, however, I could describe a tone as 1 Hz off a reference pitch or 100 cents off that pitch -- both descriptions make sense.
Given the reference pitch and the deviation in Hz, you can convert that to cents (if c is change in cents, h is change in Hz, and r is reference pitch in Hz, c=1200 log₂(1+h/r)). However, it's not possible to convert an absolute pitch to cents.

2) It's not specified, but assuming you're tuning to an A440 reference pitch:
1200 log₂(1-(2Hz/440Hz))=-7.9, so you are 7.9 cents flat.

[olivia.m19]

Ok here's my question:

1) What are cents and hertz? How are they related? Can they be converted (as in, can you answer how many cents are in 1 hz)? Why/why not?
2) Let's say I am tuning my violin. My A string is out of tune and has a frequency of 438 hz. How many cents is it off by?

1) Hertz is a measurement of cycles per second. Cents are a logarithmic measure of frequency difference, with 100 cents per semitone.
Cents can only be used as a measurement relative to some reference value, while Hertz can be relative or absolute. For example, I can have a 440Hz note (an absolute frequency), but the idea of a 100 cent note makes no sense. In terms of relative measurements, however, I could describe a tone as 1 Hz off a reference pitch or 100 cents off that pitch -- both descriptions make sense.
Given the reference pitch and the deviation in Hz, you can convert that to cents (if c is change in cents, h is change in Hz, and r is reference pitch in Hz, c=1200 log₂(1+h/r)). However, it's not possible to convert an absolute pitch to cents.

2) It's not specified, but assuming you're tuning to an A440 reference pitch:
1200 log₂(1-(2Hz/440Hz))=-7.9, so you are 7.9 cents flat.

Yep you're right! Your turn

[mjcox2000]

1)
a. Define acoustic impedance.
b. How is it useful as an analytical tool?
c. What do its imaginary and real parts each signify?
d. How is it similar to and different from electrical impedance?

2)
a. Define standing wave ratio (SWR).
b. How is SWR calculated if you are given maximum and minimum standing wave amplitudes through a tube?
c. In an electrical context, it can be useful to calculate voltage SWR and current SWR. What acoustical quantities might one want to calculate SWR for?
d. In what sort of acoustical system would one prefer high SWR? What about low SWR?

3) A narrow tube is filled with substance A, which has characteristic acoustic impedance Z1. (The tube's walls are frictionless and don't conduct any sound.) One end of the tube terminates at a speaker, and the other end terminates into substance B, which has characteristic acoustic impedance Z2. The speaker produces a plane wave audio signal which travels through the tube.
a. What fraction of the audio signal is reflected at the boundary between substance A and substance B in terms of Z1 and Z2?
b. What is the SWR in the tube in terms of Z1 and Z2?
c. Given a fixed value of Z1, what value(s) of Z2 will cause maximum power transmission into substance B? What value(s) of Z2 will cause minimum power transmission into substance B?

[mjcox2000]

1)
a. Define acoustic impedance.
b. How is it useful as an analytical tool?
c. What do its imaginary and real parts each signify?
d. How is it similar to and different from electrical impedance?

2)
a. Define standing wave ratio (SWR).
b. How is SWR calculated if you are given maximum and minimum standing wave amplitudes through a tube?
c. In an electrical context, it can be useful to calculate voltage SWR and current SWR. What acoustical quantities might one want to calculate SWR for?
d. In what sort of acoustical system would one prefer high SWR? What about low SWR?

3) A narrow tube is filled with substance A, which has characteristic acoustic impedance Z1. (The tube's walls are frictionless and don't conduct any sound.) One end of the tube terminates at a speaker, and the other end terminates into substance B, which has characteristic acoustic impedance Z2. The speaker produces a plane wave audio signal which travels through the tube.
a. What fraction of the audio signal is reflected at the boundary between substance A and substance B in terms of Z1 and Z2?
b. What is the SWR in the tube in terms of Z1 and Z2?
c. Given a fixed value of Z1, what value(s) of Z2 will cause maximum power transmission into substance B? What value(s) of Z2 will cause minimum power transmission into substance B?

Since no one has replied yet, here are answers to a few parts and hints to other parts. (Click to Show Hidden Text)

1.a. The ratio of sound pressure level to fluid flow.
1.c. Similar to electrical impedance, the real part is termed "resistance" and the imaginary part "reactance." Resistance represents the in-phase component of fluid flow, while reactance represents the out of phase component. Sound does work acting through a resistance but does no work through a reactance. Resistance comprises frictional effects while reactance comprises effects related to the inertia and elasticity of the medium.

2.b. If A is the maximum standing wave amplitude and a is the minimum amplitude, SWR=A/a.
2.d. Hint: What does SWR say about reflection vs transmission, and when would you want high reflectance versus high transmission?

3.a. The fraction of power that is reflected is ((Z1-Z2)/(Z1+Z2))^2. (Therefore, the fraction transmitted is 1-((Z1-Z2)/(Z1+Z2))^2.)
3.c. Hint: consider the electrical analogy of transmission line impedance matching.

[olivia.m19]

1)
a. Define acoustic impedance.
b. How is it useful as an analytical tool?
c. What do its imaginary and real parts each signify?
d. How is it similar to and different from electrical impedance?

2)
a. Define standing wave ratio (SWR).
b. How is SWR calculated if you are given maximum and minimum standing wave amplitudes through a tube?
c. In an electrical context, it can be useful to calculate voltage SWR and current SWR. What acoustical quantities might one want to calculate SWR for?
d. In what sort of acoustical system would one prefer high SWR? What about low SWR?

3) A narrow tube is filled with substance A, which has characteristic acoustic impedance Z1. (The tube's walls are frictionless and don't conduct any sound.) One end of the tube terminates at a speaker, and the other end terminates into substance B, which has characteristic acoustic impedance Z2. The speaker produces a plane wave audio signal which travels through the tube.
a. What fraction of the audio signal is reflected at the boundary between substance A and substance B in terms of Z1 and Z2?
b. What is the SWR in the tube in terms of Z1 and Z2?
c. Given a fixed value of Z1, what value(s) of Z2 will cause maximum power transmission into substance B? What value(s) of Z2 will cause minimum power transmission into substance B?

Let's try and revive this thread!

I'm sorry I really tried (Click to Show Hidden Text)

1b) Acoustic impedance indicates how much sound pressure is generated by a given air vibration at that frequency. The impedance of an instrument determines what notes can be played by a fingering, as well as how stable and in tune the notes are. It varies greatly based on the medium and frequency being played.
1d) Acoustic impedance is the ratio of pressure to flow; electrical is ratio of AC voltage to current (both of them measure how easily something moves through a medium). Acoustic relates to sound waves moving through things like a pipe while electrical is related to how much resistance a current encounters when moving through a wire. 

2a) SWR is the ratio of maximum amplitude to minimum amplitude.
2c) I don't really know... In an electrical setting SWR measures power transmission performance, which may be helpful for finding something relating to reflected and transmitted signal in an acoustic context
2d) A high SWR indicates high reflectance. Ideally, the SWR is 1:1 which means there is no power reflected. As harmonics are created when signal is reflected, I think you'd want high SWR if you desired harmonics and low SWR if you didn't (not sure).

3b) if [img]http://www.cdt21.com/resources/TechnicalTools/img/clip_image001.gif[/img] and [img]http://www.cdt21.com/resources/TechnicalTools/img/clip_image003.gif[/img]then [img]http://www.cdt21.com/resources/TechnicalTools/img/clip_image002.gif[/img]

3c) Maximum power is transmitted when Z2 = Z1. Minimum power is transmitted when Z2 is either 0, resulting in no pressure, or really, really large, resulting in no amplitude.

[mjcox2000]

1)
a. Define acoustic impedance.
b. How is it useful as an analytical tool?
c. What do its imaginary and real parts each signify?
d. How is it similar to and different from electrical impedance?

2)
a. Define standing wave ratio (SWR).
b. How is SWR calculated if you are given maximum and minimum standing wave amplitudes through a tube?
c. In an electrical context, it can be useful to calculate voltage SWR and current SWR. What acoustical quantities might one want to calculate SWR for?
d. In what sort of acoustical system would one prefer high SWR? What about low SWR?

3) A narrow tube is filled with substance A, which has characteristic acoustic impedance Z1. (The tube's walls are frictionless and don't conduct any sound.) One end of the tube terminates at a speaker, and the other end terminates into substance B, which has characteristic acoustic impedance Z2. The speaker produces a plane wave audio signal which travels through the tube.
a. What fraction of the audio signal is reflected at the boundary between substance A and substance B in terms of Z1 and Z2?
b. What is the SWR in the tube in terms of Z1 and Z2?
c. Given a fixed value of Z1, what value(s) of Z2 will cause maximum power transmission into substance B? What value(s) of Z2 will cause minimum power transmission into substance B?

Let's try and revive this thread!

I'm sorry I really tried (Click to Show Hidden Text)

1b) Acoustic impedance indicates how much sound pressure is generated by a given air vibration at that frequency. The impedance of an instrument determines what notes can be played by a fingering, as well as how stable and in tune the notes are. It varies greatly based on the medium and frequency being played.
1d) Acoustic impedance is the ratio of pressure to flow; electrical is ratio of AC voltage to current (both of them measure how easily something moves through a medium). Acoustic relates to sound waves moving through things like a pipe while electrical is related to how much resistance a current encounters when moving through a wire. 

2a) SWR is the ratio of maximum amplitude to minimum amplitude.
2c) I don't really know... In an electrical setting SWR measures power transmission performance, which may be helpful for finding something relating to reflected and transmitted signal in an acoustic context
2d) A high SWR indicates high reflectance. Ideally, the SWR is 1:1 which means there is no power reflected. As harmonics are created when signal is reflected, I think you'd want high SWR if you desired harmonics and low SWR if you didn't (not sure).

3b) if [img]http://www.cdt21.com/resources/TechnicalTools/img/clip_image001.gif[/img] and [img]http://www.cdt21.com/resources/TechnicalTools/img/clip_image003.gif[/img]then [img]http://www.cdt21.com/resources/TechnicalTools/img/clip_image002.gif[/img]

3c) Maximum power is transmitted when Z2 = Z1. Minimum power is transmitted when Z2 is either 0, resulting in no pressure, or really, really large, resulting in no amplitude.

Looks mostly good!

A few minor points (Click to Show Hidden Text)

2.c. Displacement and pressure are the acoustical analogues of current and voltage respectively, so these are values that it makes sense to calculate SWR for.
2.d. Very close. There's never such a thing as an [i]ideal[/i] SWR: while it's true that an SWR of 1 transmits the most power, that's not always our ideal scenario. You want high SWR for [i]resonance[/i], because high SWR means the vibrations largely stay in substance A instead of dissipating into substance B. Likewise, you want low SWR if you want to transmit sound energy into substance B.
3.b. Those equations are right, except they're in an electrical context (VSWR means voltage standing wave ratio) -- if we want to equate this with the variable names we used in the problem, [math]\Gamma=\frac{Z1-Z2}{Z1+Z2}[/math], [math]\rho=|\Gamma|[/math], and [math]SWR=\frac{1+\rho}{1-\rho}[/math]

All of the other parts look good!

Your turn!