Frequency of an open/closed pipe

In summary, the given organ pipe can resonate at three specific frequencies, but not at any other frequencies in between. To determine whether it is an open or closed pipe, calculations were performed using the equations for open and closed pipes. The resulting values for the harmonics suggest that the pipe is closed, with a fundamental frequency of 88 Hz. However, the possibility of it being open cannot be technically disproven. To improve the answer, it could be stated with more certainty that the pipe is closed, as the values for fn/f1 are consecutive integers, which is only true for a closed pipe.
  • #1
gmmstr827
86
1

Homework Statement



A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or closed pipe. (b) What is the fundamental frequency of this pipe?

Homework Equations



Open pipe: f_1 = f_n+1 - f_n
Closed pipe: f_1 = (f_n+1 - f_n)/2
n = f_n / f_1

The Attempt at a Solution



Open:
f_1 = 616 - 440 = 176 Hz >>> n = 440/176 = 2.5
f_2 = 440 - 264 = 176 Hz >>> n = 264/176 = 1.5

Closed:
f_1 = (616 - 440)/2 = 88 Hz >>> n = 440/88 = 5
f_2 = (440 - 264)/2 = 88 Hz >>> n = 264/88 = 3

So I assume the pipe is closed because I got odd integer values for the harmonics in the closed pipe test, however, I'm not sure that I technically proved it to not be open.

It would have a base frequency of 88 if it is a closed pipe, or of 176 if it is an open pipe.

How can I improve my work/answer?
 
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  • #2
The solution is correct, only you should be more positive when choosing between closed an open. The values fn/f1 have to be consecutive integers. It is true if you suppose that the pipe is closed, but fails if supposing an open pipe. The pipe can not be open.

ehild
 

Related to Frequency of an open/closed pipe

1. What is the frequency of an open pipe?

The frequency of an open pipe refers to the number of complete oscillations or cycles that occur per second in the pipe's sound wave. It is dependent on the length and diameter of the pipe.

2. How is the frequency of an open pipe calculated?

The frequency of an open pipe can be calculated using the formula f = nv/2L, where f is the frequency, n is the number of nodes or points of zero displacement in the standing wave, v is the speed of sound, and L is the length of the pipe.

3. How does the frequency of an open pipe change with length?

The frequency of an open pipe is inversely proportional to its length. This means that as the length of the pipe increases, the frequency decreases and vice versa.

4. What is the difference between the frequency of an open pipe and a closed pipe?

The main difference between the frequency of an open pipe and a closed pipe is that an open pipe has a fundamental frequency (lowest possible frequency) and all its harmonics (integer multiples of the fundamental frequency), while a closed pipe only has odd-numbered harmonics.

5. How does the frequency of an open pipe affect the pitch of a sound?

The frequency of an open pipe directly affects the pitch of a sound. As the frequency increases, the pitch also increases and vice versa. This is why longer pipes produce lower-pitched sounds while shorter pipes produce higher-pitched sounds.

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