What is the fundamental frequency of an aluminum rod?

[mcnealymt]

Homework Statement

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)

Homework Equations

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

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?

 

[TSny]

Hello.

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

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

 

[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

 

[barryj]

How did you get the length of the rod?

 

[mcnealymt]

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

 

[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.]

 

[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.

 

[mcnealymt]

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

 

[TSny]

Why not use the value in your link?

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.

 

[SteamKing]

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

According to this link: http://www.rfcafe.com/references/general/velocity-sound-media.htm

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

This link: http://www.physics.umd.edu/lecdem/services/demos/demosh1/h1-23.htm [Broken]

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