# What is the fundamental frequency of an aluminum rod?

1. Sep 2, 2013

### mcnealymt

1. The problem statement, all variables and given/known data
A longitudinal standing wave can be created in a long, thin aluminum rod by stroking the rod with very dry fingers. This is often done as a physics demonstration, creating a high-pitched, very annoying whine. From a wave perspective, the standing wave is equivalent to a sound standing wave in an open-open tube. In particular, both ends of the rod are anti-nodes. (Figure 1)

2. Relevant equations
http://session.masteringphysics.com/problemAsset/1074200/4/knight_Figure_21_55.jpg

3. The attempt at a solution

I know:

f1= v/2L

The problem is that I don't know how to calculate the speed of sound in an aluminum rod. I've ran across only one similar problem where they used:

f = v / 2 L ; where v = speed of sound

So we need to find the speed of sound in aluminum. See second web site.

f = (4877 m/s) / (2∙1.90m)
f = 128.2 s^-1 = 128.2 Hz

they then used this link to find the speed of sound in a aluminum rod
http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html

ANy ideas?!?!?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 2, 2013

### TSny

Hello.

Where did you get that value for the speed of sound in aluminum? It's not the value given in your link.

3. Sep 2, 2013

### mcnealymt

This information I found on yahoo answers:

So we need to find the speed of sound in aluminum. See second web site.

f = (4877 m/s) / (2∙1.90m)
f = 128.2 s^-1 = 128.2 Hz

4. Sep 2, 2013

### barryj

How did you get the length of the rod???

5. Sep 2, 2013

### mcnealymt

The length was given. It is 2m. My question is how do I find the speed of sound in an aluminum rod.

6. Sep 2, 2013

### TSny

Are you using a textbook? It might have a table of speeds of sound for different materials. You can also calculate the speed from the density and bulk modulus of the material.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html

[EDIT: From links given by SteamKing in post #10 below, it's Young's modulus and not the bulk modulus that should be used for the speed of sound in thin rods. Sorry for the error.]

Last edited: Sep 2, 2013
7. Sep 2, 2013

### barryj

Use this equation that you have. "f1= v/2L You know the length. Now if you know the frequency you can find the velocity, and if you know the velocity, from your second link, you can find the frequency.

8. Sep 2, 2013

### mcnealymt

Does anyone know what the speed of sound in aluminum rod is?!?!?!?!?!?!?!

9. Sep 2, 2013

### TSny

The problem with getting a value from a web search is that different sites will give somewhat different values.

That's why it would be best to get a value from your text if you can find it there.

10. Sep 2, 2013

### SteamKing

Staff Emeritus

the speed of sound in an Al rod for long. extensional waves is 5000 m/s

gives similar results.

Good old wiki confirms:
http://en.wikipedia.org/wiki/Speeds_of_sound_of_the_elements_(data_page)

Probably the last word in singing Al rods:
http://www.dougdelamatter.com/website1/science/physics/Longitudinally_Vibrating_Singing_Rod.pdf

Last edited by a moderator: May 6, 2017