Need help, beat frequencies and tuning.

[Numzie]

Need urgent help, beat frequencies and tuning.

Homework Statement

http://img144.imageshack.us/img144/4337/2aee8.th.jpg

Homework Equations

The Attempt at a Solution

You can see my attempt in the picture. I assume that beat frequencies are the absolute value of the difference between the two. The question asks for how far the tube must be extended to the 3rd decimal but i got 9cm which leads me to think its wrong since it has not decimals at all. Can someone please check my math and confirm its correct or lead me in the right way to get it correct. Thanks

 

[Numzie]

It seems as if no one could be bothered with problems involving waves and that everyone sticks to the other problems instead. Neither of my two requests for help involving waves have been seen too :(

 

[Anadyne]

Could you explain the formulas for how temperature is involved? I covered waves and stuff last year but we never talked about temperature. I agree that the diagram is correct. The calculation of the wavelength is correct. I'm a little rusty on beat frequencies though..

 

[Numzie]

Velocity of sound is affected by temperature. V_Sound{} = 331.5\times.6(Temp\degree{}C)

 

[Anadyne]

The frequency of the flute as it is now is 266.28 Hz. Since the beat frequency is 3.75Hz and it is too high, the frequency of the tuning fork is 266.28-3.75 Hz = 262.53. This is the frequency you want, so you can relate it to the intended wavelength and length of flute.

 

[Numzie]

So then 343.5/262.53=1.30842m Wavelength.
1.30842m-1.29m=.01842m
=18.42cm

18.42/2=9.21cm

Same as what i got first time around since frequency can not be negative.

 

[Anadyne]

Why are you subtracting?

In all cases: 1/2 wavelength = length of flute
1/2 (130.842) = length of flute
length of flute = 65.421
Difference = |64.5 - 65.421| = 0.921

 

[Numzie]

Oh, I see what I did wrong then. I subtracted the total wavelength of both first then divided by 2 instead of using the tube length. Thanks for all the help!