Frequency of sound waves from vibrating wire

[whatisreality]

Homework Statement

The wire has mass 250g and is tied down at both ends. It has a length of 12.50m and a fundamental frequency of 25.0 Hz. It has linear mass density.
Sound travels at 344m/s in air. Calculate the frequency of the sound waves produced when the wire vibrates at its fifth harmonic frequency.

Homework Equations

v=f lambda

The Attempt at a Solution

Just from drawing the wave, I think the wavelength of the vibration on the wire is 12.5/3.
From v=f lamda, since we know the fundamental frequency and its wavelength at this point (25m), the wire is moving at 625m/s. Which seems very fast.
My problem is, I have no idea how these relate to the longitudinal wave produced in air! Velocities aren't the same. Wavelengths are, I think...

 

[BvU]

If the fundamental frequency is a given ...

 

[whatisreality]

If the fundamental frequency is a given ...

Well, I don't know what to do with the fundamental frequency? Am I missing something really obvious?
Is the frequency of the sound wave the same as the frequency of vibration of the wire?

 

[BvU]

Definitely. Yes.

 

[whatisreality]

Definitely. Yes.

Oh. So then

625 = f* 12.5/3? And that frequency is the frequency of the sound wave. Well... that was quite silly. Thanks anyway :)

 

[BvU]

Now I'm the one who is lost. If the fundamental frequency of a wire is 25 Hz, isn't the second harmonic at 50 Hz, the third at 75, etc ? Like these guys try to tell us (for a guitar string) ?

Oh, and in your original post, you mention a drawing that causes you to think the wavelength for the fundamental frequency is 12/3. Could you explain ? Post the drawing ?

 

[whatisreality]

I meant the wavelength of the fifth harmonic is 12.5/3, because at the fifth harmonic there are 3 complete oscillations in the tube. But that was wrong because I thought it went fundamental frequency, first harmonic, second harmonic etc. So it should have been the wavelength is 12.5/2.5. And the frequency thing fits with the answer I got. I ended up with the frequency as 125Hz. So just multiplying the fundamental frequency by 5 would have been a lot quicker :)