I'm having MASSIVE confusion about harmonics and overtones of stopped pipes

[hillybilly135]

I feel like the various members of the world of physics don't agree upon what the values of n, harmonics, and overtones line up for STOPPED pipes where f n = nv / 4L

According to my physics textbook (University Physics Young and Freedman),

for stopped pipes, 3rd harmonic = n is 3 = second overtone.

HOWEVER, I got a question wrong on my second exam in General Physics because I believe my professor is one of those part of the confusion.

I copied and pasted the following from the exam solution:

QUESTION:The second harmonic (the second fundamental frequency) of a stopped (closed at one end) organ pipe is 172 Hz, the speed of sound is 344 m/s. How long is the pipe?

ANSWER GIVEN BY PROFESSOR:
The first harmonic corresponds to L = (wavelength) / 4, the second one to L = (3*wavelength) / 4

When I was doing this problem, I was immediately confused because the question asks for the SECOND harmonic of a STOPPED pipe. According to what I understand, there IS no second harmonic and n goes straight from n = 1 to n = 3.

Can some one please explain what is meant by second harmonic for a stopped pipe. Did my teacher screw up?

 

[eljose79]

Thank you for bringing this confusion to our attention. I can understand your frustration with conflicting information. However, it is important to note that the values of n, harmonics, and overtones for stopped pipes are not universal and can vary depending on the context and perspective.

In your textbook, the statement that the 3rd harmonic is equivalent to the second overtone for stopped pipes is correct. This means that when n = 3, it is the second harmonic of the pipe. However, your professor's explanation on the exam may have been referring to the length of the pipe rather than the harmonic itself. In this case, the first harmonic (n = 1) corresponds to a pipe length of one-fourth of a wavelength, and the second harmonic (n = 2) corresponds to a pipe length of three-fourths of a wavelength. This is because for a stopped pipe, the open end is at a node and the closed end is at an antinode, resulting in a quarter-wavelength standing wave.

Therefore, in the context of the exam question, the second harmonic refers to the second fundamental frequency of the pipe, but the professor's explanation refers to the second harmonic in terms of the length of the pipe. Both are correct in their respective contexts.

I hope this clarifies the confusion for you. It is important to remember that in science, there can be multiple ways of looking at a concept and different perspectives can lead to different interpretations. It is always best to consult with your professor for further clarification if needed.

 

[astrokreng]

I can understand your confusion about harmonics and overtones of stopped pipes. It is a common misconception that the second harmonic does not exist for stopped pipes. However, it does exist and is often referred to as the second overtone.

Let me clarify some terminology first. Harmonics refer to the whole number multiples of the fundamental frequency. For example, if the fundamental frequency is 100 Hz, the harmonics would be 200 Hz, 300 Hz, 400 Hz and so on. Overtones, on the other hand, refer to any frequency above the fundamental frequency, including the harmonics.

Now, for stopped pipes, the fundamental frequency is given by f = nv/4L, where n is the number of the harmonic (starting from n = 1). So, for n = 1, the fundamental frequency is given by f = v/4L. For n = 2, the frequency is 2v/4L, which is equivalent to v/2L. This is the frequency that is often referred to as the second overtone or the second harmonic. It is important to note that this frequency is NOT the same as the fundamental frequency. It is an overtone and not a harmonic.

In the question given by your professor, the second harmonic (or second overtone) is given as 172 Hz, which means n = 2. Using the formula for stopped pipes, we can write 172 Hz = 2v/4L, which can be simplified to v/2L. This is the frequency that corresponds to the second harmonic or the second overtone.

In summary, the second harmonic does exist for stopped pipes and is often referred to as the second overtone. Your professor did not make a mistake, but rather used the term second harmonic interchangeably with second overtone. I hope this explanation clears up your confusion.