Harmonic Wave Question

[SSerenity]

The person is holding one end, so this is similar to a pipe with one closed end.

I counted the 1/4th waves in the diagram. There are 3 quarter waves.

The equation:
lambda = 4L/n describes this situation, where n=odd intervals correct?

It appears the 3/4(lambda) = Len.

Len is NOT 'L' in the diagram btw.

Plugging this back into our original equation and solving for "n", we get
L4/3 = 4L/n
n = 3

Now, given that with a closed end, the 'n' values are '1,3,5,7, etc'
This means n=3 corresponds to the Second Harmonic.

But the answer is B. Why is this called the third harmonic?

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[The_Sunny_Doc]

The person is holding one end, so this is similar to a pipe with one closed end.

I counted the 1/4th waves in the diagram. There are 3 quarter waves.

The equation:
lambda = 4L/n describes this situation, where n=odd intervals correct?

It appears the 3/4(lambda) = Len.

Len is NOT 'L' in the diagram btw.

Plugging this back into our original equation and solving for "n", we get
L4/3 = 4L/n
n = 3

Now, given that with a closed end, the 'n' values are '1,3,5,7, etc'
This means n=3 corresponds to the Second Harmonic.

But the answer is B. Why is this called the third harmonic?

The value of n is the nth harmonic. 🙂 A pipe with a closed end (or a string fixed at one end) vibrates only when there's an odd multiple of 1/4 wavelength within the air column. The 2nd, 4th, 6th, etc harmonics are all missing. Because of its missing harmonics, a clarinet (a pipe with one end closed) sounds different from a flute (a pipe with both ends open), which resonates at all harmonics.

 

[SSerenity]

The value of n is the nth harmonic. 🙂 A pipe with a closed end (or a string fixed at one end) vibrates only when there's an odd multiple of 1/4 wavelength within the air column. The 2nd, 4th, 6th, etc harmonics are all missing. Because of its missing harmonics, a clarinet (a pipe with one end closed) sounds different from a flute (a pipe with both ends open), which resonates at all harmonics.

Good explanation, thank you!! you are really on top of your material! 😉

 

[The_Sunny_Doc]

Good explanation, thank you!! you are really on top of your material! 😉

No problem, and thank you. I do some physics tutoring, so it's my strong suit. Now if only gen chem was as easy to grasp. *sigh* We all have our own strengths. Best of luck with your prep!

 

[SSerenity]

No problem, and thank you. I do some physics tutoring, so it's my strong suit. Now if only gen chem was as easy to grasp. *sigh* We all have our own strengths. Best of luck with your prep!

Haha, I feel the same way. I seriously don't remember General Chem being this hard in university :s.

How did you get so good at physics? Got any tips? Just recently, my friend showed me how he uses dimensional analysis for nearly every problem. This helped so much, I cant believe it took me this long to start using it!

 

[DrBTS]

The value of n is the nth harmonic. 🙂 A pipe with a closed end (or a string fixed at one end) vibrates only when there's an odd multiple of 1/4 wavelength within the air column. The 2nd, 4th, 6th, etc harmonics are all missing. Because of its missing harmonics, a clarinet (a pipe with one end closed) sounds different from a flute (a pipe with both ends open), which resonates at all harmonics.

OOPS. edited: Asked you to clarify your explanation because I was lost but I reread it a few times and it's super succinct. Thanks!
I have a couple confusing thoughts about this:

1> How can we count the third quarter wavelength if it shows the Length from the holding position to the second node? Is my node count correct?

2> So would I be corrected in saying that for this picture there would not exist a scenario wherein the wave would exist with just two nodes (assuming that one counts the end thats held as a node?), since it's in the 4L/n where n = odd?

 

[FeinMS]

Haha, I feel the same way. I seriously don't remember General Chem being this hard in university :s.

How did you get so good at physics? Got any tips? Just recently, my friend showed me how he uses dimensional analysis for nearly every problem. This helped so much, I cant believe it took me this long to start using it!

How would you do dimension analysis for complicated units? Do you have to know what each units are composed of? For example, I can figure out that Joule=N*m from Work=force*distance, but when it comes to more complicated units, it takes longer...

 

[The_Sunny_Doc]

OOPS. edited: Asked you to clarify your explanation because I was lost but I reread it a few times and it's super succinct. Thanks!
I have a couple confusing thoughts about this:

1> How can we count the third quarter wavelength if it shows the Length from the holding position to the second node? Is my node count correct?

2> So would I be corrected in saying that for this picture there would not exist a scenario wherein the wave would exist with just two nodes (assuming that one counts the end thats held as a node?), since it's in the 4L/n where n = odd?

For a string fixed at one end, a node will always form at the fixed end while an antinode will always form at the free end. The free end could be something like, for example, a weightless metal ring sliding up and down a metal pole. Do see why the free end is the antinode and the fixed end has to be the node? You can draw your picture to see where you'd have to cut the wavelengths to get an antinode at one end and a node at the other end. 🙂 If I try to cut the wavelength at 2/4 (=1/2 wavelength), I would get a node at one end and a node at the other end.

There would be a wave with two nodes at the third harmonic. At a length of 1/2 wavelength you get the other node. Just to remember that you have to add both a node and an antinode to make next possible wavelength for a string fixed at one end or a pipe closed at one end, or else you wouldn't have an open/free end any longer! That why you can only get harmonics at the odd multiples of 1/4 wavelength.

Here's a graphic I altered a bit from Physics for Scientists and Engineers for my notes:

How would you do dimension analysis for complicated units? Do you have to know what each units are composed of? For example, I can figure out that Joule=N*m from Work=force*distance, but when it comes to more complicated units, it takes longer...

Memorize all the derived units for E&M. Amps, Watts, Joules, Ohms, Volts, all that good stuff. It's a pain, but it can help to point you toward the right answer when you're not sure how to solve something.

Haha, I feel the same way. I seriously don't remember General Chem being this hard in university :s.

How did you get so good at physics? Got any tips? Just recently, my friend showed me how he uses dimensional analysis for nearly every problem. This helped so much, I cant believe it took me this long to start using it!

D.A. can help. That's a great tip for those plug and chug problems.

For me, the key was to work with a lot of illustrations and diagram. Having an artistic streak helps. It's quite the visual-spatial science, so if you can recall the picture you drew and "see" the answer to the problem in your mind without having to think through any of the steps, it will save you time on the test. If you have spent time drawing, or putting together a collage for a concept, your brain has had to build your understanding from scratch, so it sticks with you much longer than if someone told you how to do a problem, or if you just looked at the formula and plugged in numbers.

Another tip is to study related concepts together, like fluids and electronic circuits. It's all about the relationships with physics. 🙂