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Old Jun 24th 2017, 06:02 PM   #1
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Need some help please with resonant lengths.

Hi,

I'm just beginning physics and I'm having some trouble. Even when I get the right answers they just don't feel correct or entirely complete. I'm just hoping someone can let me know if I did this right, and what I could do to add to it if necessary. I apologize for the messiness I couldn't find symbols, I hope it is clear enough.

A hollow tube chime is open at both ends, the chime is 0.54m in length, the speed of sound is 346m/s.

Finding the third resonant length and it's frequency:

L = wavelength/2
0.54m = wavelength/2
2(0.54m) = wavelength
1.08m = wavelength


third resonant length: L3

L3 = 3(wavelength)/2
L3 = 3(1.08m)/2
L3 =1.62m

third resonant length: 1.62m

f = v/wavelength
= 346/1.62
= 213.58 Hz

frequency of third resonant length: 213.58 Hz

Thanks very much for your help.
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Old Jun 24th 2017, 09:04 PM   #2
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for an open-ended tube of length $L$ ...

$f_1 \implies L = \dfrac{\lambda}{2} \implies \lambda = 2L$

$f_2 \implies L = \lambda$

$f_3 \implies L = \dfrac{3\lambda}{2} \implies \lambda = \dfrac{2L}{3}$

$f_4 \implies L = 2\lambda \implies \lambda = \dfrac{L}{2}$

Note the sequence for values of $\lambda$ ...

$\dfrac{2L}{1}, \, \dfrac{2L}{2}, \, \dfrac{2L}{3}, \, \dfrac{2L}{4}, \, ...$

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Old Jun 24th 2017, 09:47 PM   #3
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I originally didn't see how that helped me at all, but I see now what I did wrong. Thank you for your help.
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frequency, hertz, lengths, resonant, wave



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