# Fundamental Frequencies and Standing Waves

1. Jun 8, 2006

### Lil ze

Evening,

Ive been having some trouble with questions about fundamental frequencies and labelling nodes and anti nodes in an air column.

for example :a tuning fork is placed above a glass tube and then the sound of the air column is adjusted by raising or lowering the glass tube in the water until a loud sound is heard.

I dont understand where (and how) the Nodes and Antinodes are. Secondly, isnt the fundamental frequency half a wavelegnth ie distance between 2 nodes.

thanks a lot again

2. Jun 8, 2006

### Hootenanny

Staff Emeritus
3. Jun 8, 2006

### Staff: Mentor

The fundamental frequency in this context is the lowest frequency that causes a resonance (and hence standing waves). Picture a guitar string. When plucked just right, it will vibrate at its fundamental frequency, which is where the two nodes are at the ends (obviously since the string is tied to the guitar solidly at the ends), and there is one single node (the maximum amplitude part of the string side-to-side excursion) in the middle of the string. That is the fundamental mode, and the lowest frequency standing wave that you can form in that physical situation.

But think about what that string looks like as it vibrates back and forth. When it's at maximum amplitude one way, what is its shape? How much of a sine wave does it look like? How long would a full sine wave cycle be where part of the full cycle matches the shape of the guitar string? You have it mostly correct in your question above, but don't say "the fundamental frequency is half a wavelength". Say instead that at the fundamental mode, there is half a wavelength between the two nodes, and an antinode in the middle. So if you know the velocity of propagation of the wave on the string (from the string tension and linear mass density), you can figure out what the fundamental frequency is, because you know how long a half a wavelength is. Makes sense?

4. Jun 8, 2006

### Lil ze

Thanks you guys, that really did help sort my probs out,iam starting to get my head around the questions.

Hootenanny, that link was great, had exactly the practical applications i was looking for, and berkeman thats helped me picture what it looks like :D

I had a look on that website if there was anything about periods and oscilloscope graphs on the website, but it doesnt seem to be there. do u know any other good physics revision websites about ? there really dont seem to be many. It would make more practical sense if i could look up the website then come here if iam stil stuck :D

cheers guys :D

5. Jun 8, 2006

### Hootenanny

Staff Emeritus
What type of things are you looking for?

6. Jun 8, 2006

### Lil ze

Firstly what is a period and whats its relavence, and then ive had many questions asking me to draw what would be on an an osciloscope. With a certain time base and amplitude.

Oh and slightly off topic, in the symbol for the electrical cell (---|i--) which one is the postive one and which one is the negative ?

thanks

7. Jun 8, 2006

### Hootenanny

Staff Emeritus
I can't think of any websites off hand. And I don't like drawing oscillographs myself, so I'm no help there I'm afraid.

As for the time period (T), it is the time taken for one wavelength to pass a fixed point. It is the reciprocal of the frequency;

$$T = \frac{1}{f}$$

Hopefully, now you've seen the relationship between the time period and frequency you can see its relavence.
The longer one is the positive one, the shorter one is the negative one.

8. Jun 8, 2006

### Staff: Mentor

For fun with oscilloscopes, go to the LeCroy website, click on a scope family, and click on Test Drive....

http://www.lecroy.com/

9. Jun 9, 2006

### Lil ze

Hey guys, had my physics exam today and it went well, nothing on periods or air columns! so hopefully ive not screwed up and really nailed it to get a good A. thanks for ur help guys,it was invalueable. (Y) :D

10. Jun 9, 2006

### Hootenanny

Staff Emeritus
It was a pleasure, I'm gald that you felt it went well. Fingers crossed for the results! Be sure to let us know