# Homework Help: Theoretical Resonance

1. Mar 5, 2006

### Alec

I made an experiment in a tube, 75 centimeters.
There was sand in it so I could distinguish one wave length.
the biggest one I got was 0.335 meters at a frequency of 480Hz and the smallest was 0.07 meters at a frequency of 2000 Hz.
I calculated the resonance in the tube as 1.5 meters as the biggest and 0.3 meters as the smallest.
I'm now wondering why this differs so much from my measuring in the tube?

2. Mar 5, 2006

### sebas531

how did you calculate the 1.5m and the .3m?

3. Mar 5, 2006

### Alec

I used the formula L = lambda / 2 for the normal tone.
L = lambda for 1st over tone and L = 3 * lambda / 2 for 2nd over tone and finaly L = 5 * Lambda / 2 for 3rd? over tone (I got help in another thread).
L being the length of the tube 0.75 meters.

4. Mar 5, 2006

### sebas531

Could you explain your lab. It sounds as if this pipe was a closed pipe resonator, but i need you to explain the lab meaning what you did in order to change the lengths of the pipe with the sand.

5. Mar 5, 2006

### Alec

The tube was half open, it had a tonegenerator plugged into it, and then there was sand. Once you turned the frequency up the sand began to vibrate because of the sound waves that was sent out. You were able to distinguish two nodes and measure the distance between them. Once you turned up the frequency the nodes got closer to eachother (only on certain frequencies), we never got it really high 2000 Hz was the highest.
Do you see the scenario now?

6. Mar 5, 2006

### sebas531

do you know what it means to resonate?

7. Mar 5, 2006

### Alec

No, sorry I don't.

8. Mar 5, 2006

### sebas531

another question and i will try to help, did you change the lengths of the tube at all?

9. Mar 5, 2006

### Alec

No, never, it's determined to 0.75 meters. (made of glass and impossible to change). Thank you!

10. Mar 5, 2006

### sebas531

well, i dont have to much time right now, and it is taking you a while to reply, so ill explain what resonance is in my own words and ill explain it to you in a way for you to understand. Whenever a sound wave goes through a tube it will reflect of the end, in both an open pipe and closed pipe resonators. If the high pressure wave reflects back and reaches the source(what creates the waves) at the same time that another wave is leaving then those two waves, the reflected and the one leaving will reinforce eachother and you will be able to hear a louder sound at that point it is said that the air column is in resonace with the source.

11. Mar 5, 2006

### sebas531

when the reflected wave and the wave leaving meet they will creat a standing wave, just for your own info

12. Mar 5, 2006

### sebas531

well, since its one open end and one close end, its a closed pipe resonator for what it seems. well, an closed pipe resonator has a node at the open end and an antinode at the close end. The shortes column of air that can have that is 1/4 wavelenght long. one must use the equation F=n(v/4L) where f is the frequency, n is the number of harmonics it has to be odd numbers though, v is velocity of air, and L is the length. Since you didnt give me what the temperature was then im going to say that is room temperature in which sound travels at 343 m/s.

so in order to calculate where there will be resonance for a frequency you must change the equation to: L=n(v/4F)

13. Mar 5, 2006

### sebas531

sorry about that v is the velocity of sound. I was thinking about the air temperature.

14. Mar 6, 2006

### Alec

Thanks for the replies!
I have now only three small questions left I've been wondering about:
Why does the cork dust move in Kundts tube?
When calculating the velocity of sound, why does it differ so much? Is it because I measured bad?
And why does it differ so much from the "ideal" resonance?

15. Mar 6, 2006

### sebas531

I dont really understand what you are asking. Could you state your question in a different way?

well, you have not told me how you calculated the speed of sound. Tell me what you did and then I might be able to tell you why.

Good question. When i studied sound, i came across a lab that eventhough it varied in process was still about the same subject. Well, when i first did the lab i got really far answers from the accurate ones. I asked myself and my teacher why but we never knew. But i then made some calculations using the formula that i gave you before and when to check resonance again in the lab around those points and i got it really close. sorry but i cannot help you out with these one.

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