Calculate fundamental overtone and length of tube

In summary, the conversation discusses calculating the fundamental overtone and length of a tube open at both ends, given three consecutive harmonics at 438 Hz, 584 Hz, and 730 Hz. The equations given are L=lambda/2 x n and v=f x lambda, and it is mentioned that harmonics in this type of tube are integer multiples of the fundamental frequency. For part A, the difference between the given frequencies can be used to find the fundamental harmonic, and the first overtone can be found by multiplying the fundamental frequency by 2. For part B, the speed of sound in air at 20°C (343m/s) can be assumed to simplify calculations.
  • #1
bookerdewitt
15
0

Homework Statement


It is observed that a tube open at both ends exhibits harmonics at 438 Hz, 584 Hz, and 730 Hz.
A) Calculate the fundamental overtone of the tube.
B) Calculate the length of the tube.



Homework Equations


L=lambda/2 x n, v = f x lambda



The Attempt at a Solution


I know that the fundamental overtone is the second harmonic so n would be 2 but to calculate the frequency I would need to know the velocity and wavelength and I don't see how I can get those.
 
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  • #2
A)Well, in this instance, you are given three consecutive harmonics at 438Hz, 584Hz, and 730Hz. Besides the equations that you are given, you also know that harmonics in this open tube are integer multiples of the fundamental frequency. So, you can easily calculate the difference between each of the given frequencies to find the fundamental harmonic. From there, you can find the first overtone by multiplying the fundamental frequency by 2.
 
  • #3
B) For this part, it looks like they want you to assume the speed of sound to be 343m/s (speed of sound in air at 20°C). If this is the case, then your calculations should be relatively simple.
 
  • #4
Thanks a lot.
 
  • #5
What calculation is to be used for part A and part B?
 

What is the fundamental frequency of a tube?

The fundamental frequency of a tube is the lowest frequency at which the tube can vibrate and produce a standing wave. It is also known as the first harmonic.

How is the fundamental frequency of a tube calculated?

The fundamental frequency of a tube can be calculated using the formula f = v/4L, where f is the frequency, v is the speed of sound, and L is the length of the tube. Alternatively, it can also be calculated using the formula f = 1/2L, where L is the length of the tube.

What is the overtone of a tube?

The overtones of a tube are frequencies that are integer multiples of the fundamental frequency. These frequencies produce standing waves with more nodes and antinodes than the fundamental frequency.

How is the overtone of a tube calculated?

The overtone of a tube can be calculated using the formula f = nf, where n is the overtone number and f is the fundamental frequency. For example, the second overtone would have a frequency of 2f, the third overtone would have a frequency of 3f, and so on.

How does the length of a tube affect its fundamental frequency and overtones?

The fundamental frequency of a tube is inversely proportional to its length. This means that as the length of the tube increases, the fundamental frequency decreases. The overtones, on the other hand, are directly proportional to the length of the tube. This means that as the length of the tube increases, the overtones also increase.

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