Calculate fundamental overtone and length of tube

AI Thread Summary
To calculate the fundamental overtone of a tube open at both ends, the differences between the given frequencies (438 Hz, 584 Hz, and 730 Hz) can be used to determine the fundamental frequency, which is the basis for finding the first overtone. The fundamental overtone corresponds to the second harmonic, calculated by multiplying the fundamental frequency by 2. For calculating the length of the tube, the speed of sound in air (assumed to be 343 m/s) is used along with the formula L = λ/2 x n, where n is the harmonic number. By applying these principles, the required values can be derived. Accurate calculations will yield both the fundamental overtone and the tube's length.
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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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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.
 
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.
 
Thanks a lot.
 
What calculation is to be used for part A and part B?
 
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