Please help me with my physics science project!

[Josh21]

Hi, for my 9th grade Physical Science class, we have to create a science project and I decided to use the project plan at this link (because i play guitar):
https://www.sciencebuddies.org/science- ... ?from=Home

The only requirements for the project is that it has to be related to physics and on "Science night" we have to perform a visual demonstration of the project (along with a tri-fold board). Anyhoo, I am a slow learner and I don't quite understand exactly what "nodes" and "wavelengths" are....I have read up on these topics online but I got easily confused. Please explain to me what these terms mean in the simplest words possible. Also, I especially don't understand this step from my experiment:

Use your knowledge of standing waves to calculate where the following are located for each string:

1. Location of node(s) and antinodes for the 2nd, 3rd, 4th, etc. harmonics of each string.
2. Frequencies (pitches) for the 2nd, 3rd, 4th, etc. harmonics of each string.

Please help me, Thanks in advance!

[deleted-71586]

Hi Josh21,
If you are the guitarist that you claim to be, then you do understand the vib's that are being asked in this science project. On your guitar the first harmonic is the maximum wave length and the maximum distance the guitar string is allowed to naturally vibrate; see http://www.glenbrook.k12.il.us/gbssci/P ... 11l5b.html. The nodes are at "zero string motion" during vibation and the antinodes are at maximum string motion during vibation. You change the frequency of the sound by changing the length of the string vibration. Good luck.
John

[Josh21]

Thanks for the help John, but I am not a great guitarist, I just play for fun. I now somewhat understand what nodes and anti nodes are . But I also have another question: I don't understand this part of the experiment:

Measure the length of the strings on your guitar (in cm), between where they contact the bridge and where they contact the nut.
Measure the location of each of the pickups for each string.

Won't each string be the same length from the bridge to the nut? And be the same distance away from the pick-up???

In addition, for the following questions:

1. Which harmonics have nodes near the pickup?
2. Which harmonics have antinodes near the pickup?
3. Which harmonics will contribute most to the sound produced by each pickup?
4. Which harmonics will contribute least to the sound produced by each pickup?

Please explain these questions the best you can so I can follow up with the experiment (especially numbers 1and2).

Lastly, what do you think is the best way to do this experiment....On my tri-fold I will probably write a section about the basic terms, but how do you think i should present the data,..... 1 big,long chart?

Thanks so much for your help, you're really a life saver !

-Josh

[deleted-71447]

Hi Josh 21,
I'll try to fill in for John as best as I can. It sounds like those instructions are for an electric guitar with a Fender style bridge/ saddle that allows for adjustment of the lengths of individual strings. You can see an example in this photo:
http://www.marchione.com/2611503.jpg
Each bridge section is at a slightly different position, allowing for different length strings. What sort of guitar are you using?

This section of the webpage you've been using has the information on nodes and antinodes that should help you to answer the other 4 questions.
http://www.glenbrook.k12.il.us/gbssci/P ... 10l4d.html
Please let us know if you run into any problems.

Chris

[Josh21]

Okay, thanks Chris! The website on nodes you showed me helped me a lot!

My guitar is an SG with a bigsby-tremolo bar. As far as I know, you cannot adjust the length of individual strings with the type of bridge i have. Each string is the same length from the bridge to the nut and the same distance away from the pick-up(s). I took a photo of my guitar so you can see what I mean:

http://img02.picoodle.com/img/img02/4/4 ... 97b204.jpg

Is a guitar with a Fender style bridge necessary for this experiment? Is there anyway I can still do the experiment without buying a new guitar?

Also, how do you think I should demonstrate my project? On "Science Night" we have to perform a demonstration that relates to our experiment. It has to be around 5 minutes long and it should be interesting and understandable for people that come by. Any ideas?

Lastly, how should I organize the data from the results of the experiment? What do you think is best, a chart,graph etc.?

Thank you so much

[deleted-71588]

In quickly reading the orignial project, I didn't see any reason why the type of bridge is important. You still need to measure the length of each of the strings. Even with an inline bridge, the bridge is not guaranteed to be perfectly parallel to the nut in all positions of the tremolo bar. If the strings all turn out to be the exact same length to the precision that you can measure them at a given tremolo bar setting, so be it. The project was just set up to deal with the more challenging case of a complex bridge.

IMO: The important thing that is hard see in a demonstration at any distance is the standing wave vibration nodes. Maybe the use of a video recording of a close up of this or a live closeup would be appropriate.

Charts and graphs are good. Try seeing how a preliminary crude chart or graph works in explaining it to a parent, friend, grandparent, or neighbor that isn't really into your project but is interested helping you. If the visual aid makes it fast and easy to convey the important points, then you have a great presentation. If not, maybe you need a different chart or graphical presentation.

[deleted-71447]

Hi Josh,
Your guitar is fine for this project. Like Craig said, even if the distance between nut and bridge is the same for each string, you can still measure the length of one string. In your photo, it looks like the contact points at the bridge are slightly offset for each string (which would give different string lengths), but maybe it is the angle of the photo.

A "slinky" demonstration would be one possibility for you. You can lay a slinky on the floor, stretched between two people (or between one person and a fastened point), and then shake the end(s) of the slinky to produce different standing wave patterns. Here are some photos of this type of demonstration:
http://hyperphysics.phy-astr.gsu.edu/Hb ... lnksw.html

Chris

[Josh21]

Thanks loads for your help Craig and Chris, and the slinky was a great idea ! Anyways, I was starting the actual experiment, and I had trouble with Number 3 B:
Calculate the Frequencies (pitches) for the 2nd, 3rd, 4th, etc. harmonics of each string.

I know I have to use this formula: speed = frequency • wavelength , but I don't know how to get the speed of the waves. So if i was trying to find the frequency of the 1st harmonic on my low E string, 1.27 would be the wavelength because .635 meters is the length of the string times 2 = 1.27. But where would I go from there to determine the frequency? I have no clue as to how to find the speed of the string!

Also, I found this site that explains harmonics very well:
http://www.guitarlessonworld.com/lessons/lesson46.htm

According the fretboard near the top of the page, there are 8 harmonics per string, and there are 6 strings. so for my experiment should I be finding the frequency for 48 different harmonics? Am i lost or am i on the right track?

Any help is great appreciated

[deleted-71447]

Hi Josh,
I'm glad you like the slinky demonstration.
For those calculations, you first need to determine the frequency of the string. Do you have a electronic tuner that you can use to measure the frequency? If you don't own one, you can probably borrow one or buy one. Once you know the frequency and wavelength of the first harmonic, you can calculate the speed of the first harmonic. The speed is the same for all the harmonics, so you can use the speed and wavelenghts of each harmonic to calculate its frequency. Example calculations are shown on this web page, about half way down the page:
http://www.glenbrook.k12.il.us/GBSSCI/P ... 11l4d.html
Keep up the good work!
Chris

[Josh21]

Actually, I do own an electronic tuner, but it does not tell you the frequency. Instead, I downloaded this program called MuseBook Tuner the that displays the frequency when I play my guitar in front of a mic. But you never answered my other question: For my experiment should I be finding the frequency for 48 different harmonics?

[deleted-71447]

Hi Josh,
I'm glad you figured out the frequencies. That would be fine to calculate the frequency of the 8 harmonics on all 6 strings, although I'm not sure whether that will be interesting to you or to your audience. Often, a the project web page like this one will serve as a starting point from which to develop your own ideas and explore your own questions. I would recommend that you think about a testable hypothesis related to waves, frequency, harmonics, etc, and then think about measurements you could make to to test that hypothesis.
Chris

[Josh21]

Thank you once again Chris. Could you be so kind as to give me a sample test hypothesis I can use? I have no clue what to do....science is my worst subject and my teacher is not any help. I ask her for help and she says that she cannot help me with the project. Remember: the project has to be related to physics, but we haven't learned a single thing about physics yet....thats what makes it so hard. I have gotten all the frequencies but I don't know what to do with this information! I am totally freaking out because I have to do a 7 minute demonstration for her and I still haven't got a decent demonstration. I like the slinky idea...but is there bleep i can do with my actual guitar to demonstrate the project? I'm allowed to bring in my guitar and amp for the demonstration.

I still don't quite get how I can find the location of node(s) and antinodes for the 2nd, 3rd, 4th, etc. harmonics of each string. I know what nodes and antinodes are...i just don't know how i can find the location of them. Can you please give me specific instructions on how to do so?

thank you so much for your help, you truly are a life saver

[deleted-71447]

Hi Josh,
For a hypothesis, you now know enough about wavelengths, velocities and frequencies to come up with many questions that you could answer. A simple question for you would be bleep like "How do harmonics affect the frequencies of wave vibrations of guitar strings"? You could present your calculations of the frequency of each harmonic and then compare those values to measurements taken using your computer software. If you have more time available, a more complicated (and maybe more interesting) example would be to test a hypothesis about how the tension of a string affects the velocity and frequency of the strings. If the tension is twice as large, is the velocity also twice as large? For this experiment, you could measure the tension of a string and compare that to the velocity and frequency of waves on that string. You would need to build or borrow an apparatus, which could be similar to the one on the second page of this document, which also explains a little about tension:
http://www.physics.rutgers.edu/~jackph/ ... 8_ver1.pdf

For your demonstration, I'm sure you will do great. You chose a topic that has some personal interest for you, and that interest will be clear to the teacher and other students. I do not know what your teacher expects for those 7 minutes, but I assume that some of the time will be explaining the background of your experiment to the other students who aren't yet familiar with waves. For the demo, there are lots of possibilities. You could play some sort of game where you play an E, tell the students the frequency, then play some other notes and harmonics and ask them to guess the frequencies. You could try (I haven't tried this and don't know if it will work) shining a laser pointer beam across (perpendicular to) a string and onto a screen, then pluck the string to show how the vibrations of the string disrupt the laser beam image on the screen. If that works, you could possibly position the laser beam at the mid point of the string so that when you play a regular note, there is a lot of vibration, and when you play a second harmonic, there is less vibration at that node location (see below).

For finding the location of nodes and antinodes, keep in mind that the nodes are evenly spaced along the string (in theory, anyway). Refer to those pictures on the the web site I gave earlier, http://www.glenbrook.k12.il.us/gbssci/P ... 10l4d.html
For the first harmonic, there exists one antinode at the mid-point along the length of the string and two nodes at the fixed ends of the string. For the second harmonic, the center of the string is now the location of a node and there are two antinodes located at the midpoints between the nodes. The nodes and antinodes are evenly spaced, so for example for the second harmonic the distance between a node and the nearest antinode is 1/4 the length of the string. It will probably help to look at and/or draw some diagrams. Make sure to do the same in your presentation when you explain all this to the other students.

You'll do great! It's going to be a very nice project.

Chris

[Josh21]

Thank you so much for your help once again Chris! and thanks especially for explaining the nodes/antinodes! I like what you were saying about the laser beam...but I don't get what the "screen" is...but that would be really cool for the demonstration if I could figure it out. Also, do you know where I could purchase a tuner that shows the frequency of the note so i could bring it in for the demonstration? i checked my local music store but they didn't have any....do you happen to know of any websites that would carry that product?
Thanks a million!
-Josh

[deleted-71447]

Hi Josh,
You're welcome. By "screen" I meant some sort of screen typically used for a projector. It could just be a white wall, or a white piece of paper.

For a mobile tuner, you have a few choices:

1) buy or borrow a fancy tuner that displays hertz.
http://www.korg.com/gear/info.asp?a_prod_no=DTR2000

2) Use a regular tuner with a display in cents, and then convert to hertz
Here is an explanation of hertz and cents
"HERTZ OR CENTS
Tuners behave like frequency counters, measuring the frequency of an instrument's notes. Scientific frequency counters measure frequency (or cycles per second) in Hertz (Hz), but this can be a bit unintuitive for musical purposes, and so Cents are used where one semitone is split into 100 equal units, each being one Cent. If you are out of tune, the display will indicate how many Cents out you are."
http://www.korg.com/service/downloadinfo.asp?DID=1326
A cents to hertz conversion table is here:
http://home.broadpark.no/~rbrekne/refer ... ts-hz.html

3) If you have access to a Smartphone, there are some tuner programs available that will display in hertz. If interested, try a search for "HandDee GTuner (SP) guitar tuner 1.2.1"

[Josh21]

Thanks for helping me out Chris, I am trying to find someone who owns a Smartphone, but no luck....

Anyways, I found the frequency of all the harmonics of each guitar string, I used this website to figure out which frets the harmonics are at: http://www.guitarlessonworld.com/lessons/lesson46.htm

Here are my results:
1st Harmonic 2nd Harmonic 3rd Harmonic 4th Harmonic 5th Harmonic 6th Harmonic 7th Harmonic 8th Harmonic
e B: 246.94 Hz G♯: 1661.22 Hz E: 1318.51 Hz B:987.77 Hz G♯: 1661.22 Hz E: 659.26 Hz G♯:1661.22 Hz B: 987.77 Hz
B F♯: 185 Hz D♯: 1244.51 Hz B: 987.77 Hz F♯: 739.99 Hz D♯: 1244.51 Hz B: 493.88 Hz D♯: 1244.51 Hz F♯: 739.99 Hz
G D: 73.42 Hz B: 987.77 Hz G: 783.99 Hz D: 587.33 Hz B: 987.77 Hz G: 392 Hz B: 987.77 Hz D: 587.33 Hz
D A: 110 Hz F♯: 729.99 Hz D: 587.33 Hz A: 440 Hz F♯: 739.99 Hz D: 293.66 Hz F♯: 739.99 Hz A: 440 Hz
A E: 82.41 Hz C♯: 554.37 Hz A: 440 Hz E: 329.63 Hz C♯: 554.37 Hz A: 220 Hz C♯: 554.37 Hz E: 329.63 Hz
E B: 493.88 Hz G♯: 415.3 Hz E: 329.63 Hz B: 246.94 Hz G♯: 415.3 Hz E: 164.81 Hz G ♯: 415.3 Hz B: 246.94 Hz


Here are the Relationships I found out:
-The 1st harmonic has one fourth the frequency of the 4th harmonic.
- The 2nd, 5th, and 7th harmonics have the same frequency.
-The 4th and 8th harmonics have the same frequencies.
-The 6th harmonic is double the frequency of the frequency of that open string.
-The frequency of the 3rd harmonic is double the frequency of the 6th harmonic.

Could you please help me analyze these results and explain why these relationships occur? I can't make much sense of them....please reply as soon as possible because I am doing a demonstration of the project on Friday. THANKS SO MUCH!

[deleted-71447]

Hi Josh,
Friday, as in today? If so, I hope your presentation went well, and sorry I didn't get to offer help in time. Let me & the other experts know if you still need info.
Chris

[Josh21]

No of course not today ! I meant next friday !

[deleted-71447]

Good! I'm glad there is some extra time left.
In the table I see that each row is one of the 6 strings, and I see eight frequencies listed for each string. There are a few important issues:
(1) The order of the notes & frets shown in that page you linked is not the same as the order of the harmonics. For example, the first harmonic is an open string. The second harmonic is played by touching the string at the 12th fret. Here is another web page that makes this a little clearer in terms of frequencies, frets, and harmonics:
http://www.igdb.co.uk/pages/techniques/harmonics.htm
There is a figure about halfway down the page that shows which frets can be used to play certain harmonics.
(2) For a single string, you should not have multiple harmonics with the same frequency. It looks like the values in your table are from a table of notes & pitches without consideration that some of the notes shown on the diagram are in different octaves. The same note in two different octaves does not have the same frequency. I strongly recommend running the calculations so that you can understand the physics at work. I or others here can help with that if you want.
(3) Are you expected to perform a scientific experiment, as opposed to a research project? This is currently more of a research project. If you are expected to perform an experiment, you will probably get higher marks if you take some measurements to answer a scientific question.
For more information about the scientific bleep, look here:
http://www.sciencebuddies.com/science-f ... thod.shtml

[Josh21]

Oh wow that changes everything! The website you showed me was excellent! But, it only shows you up to the 3rd harmonic....how would I find the 4th,5th, etc harmonics? What frets should I play at to play the other harmonics?

"The same note in two different octaves does not have the same frequency."
I had no idea! So you're saying that every harmonic on a string should have different frequencies? Also, could you please elaborate on those calculations....how would I find the frequency by using calculations?

This is the project: We have to create an experiment, research the topic, use a tri-fold board to explain and show the experiment, and them do a demonstration on the project to whoever walks by on Science Night. This is my question: "How do harmonics affect the frequencies of wave vibrations of guitar strings"?
What do you mean by "take some measurements to answer a scientific question."? If you mean experimental design, I already did that.

-Josh

Also, if you happen to know any free MAC programs that displays the frequency of the notes, please inform me! thanks!

[deleted-71447]

Hi Josh,
Thanks for the clarification. That is very helpful.
Please take another look at that web page - about halfway down under "natural harmonics" you will see a figure that includes some red lines superimposed on a photo of a guitar neck and a table of frets, harmonics, and octaves. The 2nd, 3rd, 4th, 4th, 6th, and 7th harmonics are shown. The exact fret locations are shown, including harmonic node locations that are between frets. The 8th harmonic is not shown, but I don't see any problem with just using the first 7.

Yes, every harmonic on a string should have a different frequency. The equation you will need is this:
v = fλ
v is velocity
f is frequency
λ is wavelength
For your purposes, you can assume that the velocity of the string does not change (see http://www.physics.rutgers.edu/~jackph/ ... 8_ver1.pdf for more info). By measuring the frequency of the open string and the length of the string, you can calculate the wavelength (2x string length) and the velocity. Then, you can calculate the wavelength of each harmonic (as demonstrated on https://www.sciencebuddies.org/mentorin ... p053.shtml) and use each wavelength along with the string velocity to calculate the frequency of each harmonic. You'll see that as the wavelengths get shorter, the frequency gets higher.

I think your scientific question is fine. My recommendation is that you should evaluate your hypothesis (answer your question) based on measurements, for example by using a computer program to measure the frequency of the various harmonics. Once you have those measurements, then it would make an interesting comparison to see if those values are the same as the values predicted from calculations or from a table of frequencies. I would not recommend using calculated or table values as your primary source of "data" to evaluate your hypothesis.

I don't know any mac programs, but I bet they are out there. Maybe an internet search for "guitar tuner program mac" will yield some results.

Chris