Length of a Closed Air Column

  • Thread starter hamza2095
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  • #1
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Homework Statement


The resonant length of a closed air column at the first resonance is 0.375m, what is the wavelength when at 4th reasonance

Homework Equations




The Attempt at a Solution


1/4λ=0.375m
λ=1.5m
1.5m/7 = 0.214m
 

Answers and Replies

  • #2
Merlin3189
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I agree with your wavelength at first resonance and your answer.
 
  • #3
TSny
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As third poster, I second your fourth resonance answer.:smile:
 
  • #4
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As third poster, I second your fourth resonance answer.:smile:
This was a question on a test, the way I got the answer was knowing v/f=λ and i knew that 7/4 of the wave fits in the 4th reasonance and 1/4 in the first, meaning the frequency is 7x more. I assumed the the velocity was 1.5m/s and the frequency was 1hz so 1.5ms/1hz = 1.5m, after that i mutliplied the 1 hz by 7 to get the answer. Is there an easier way to go about this?, I had trouble with it because the neither the speed of sound or frequency was given.
 
  • #5
TSny
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i knew that 7/4 of the wave fits in the 4th reasonance
That's the key.

Note that the 0.375 m given in the problem represents the length of the pipe. So 7/4 λ = 0.375 m.

You don't need to assume a value for f.
 
  • #6
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Ohhh okay I see, thank you. I knew there was an easier way to look at it.
 
  • #7
TSny
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Good. Drawing pictures for these types of problems is always a good thing to do.
 
  • #8
Merlin3189
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Absolutely agree with TSny, draw diagrams. I did.

You may notice my first post is oddly worded, because you tricked me into thinking you'd done the second part wrongly and I had to edit it!
I had ##\frac{λ_1}{4}=0.375## and ##\frac{7λ_2}{4}=0.375## so when I saw your /7 I thought at first you'd missed out the 4.
 

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