Displacement nodes for overtones

[vel]

Homework Statement

Standing sound waves are produced in a pipe that is 1.80 m long.
1) If the pipe is closed at the left end and open at the right end, determine the locations along the pipe (measured from the left end) of the displacement nodes for the first overtone.
2) If the pipe is closed at the left end and open at the right end, determine the locations along the pipe (measured from the left end) of the displacement nodes for the second overtone.

Relevant Equations

(4 / 3) * L = lambda
1st overtone: L / 4, (3 * L) / 4
2nd overtone: L / 6, (3*L) / 6, (5 * L) / 6

(4 / 3) * (1.8) = 2.4 = lambda
1st overtone: 2.4 / 4 = .6; (2.4 * 3) / 4 = 1.8

 

[sysprog]

Hey, @vel, please use $\LaTeX$ for mathematical expressions $-$ there's a link to a guide at the lower left area just below the reply box $-$ using $\LaTeX$ makes what you are expessing more clear for your fellow PF members.

 

[vel]

Hey, @vel, please use $\LaTeX$ for mathematical expressions $-$ there's a link to a guide at the lower left area just below the reply box $-$ using $\LaTeX$ makes what you are expessing more clear for your fellow PF members.

I read through it, but I'm more often than not on my phone (especially for drawings/diagrams), so using LaTeX would mean I couldn't see my own equations properly. I can space them out more, though

 

[sysprog]

I read through it, but I'm more often than not on my phone (especially for drawings/diagrams), so using LaTeX would mean I couldn't see my own equations properly. I can space them out more, though

It's obvious that using a phone keyboard instead of a full-sized keyboard makes typing more cumbersome, and of course it's easier to post a screenshot of something previously hand-written and then photographed on your phone's camera than it is to on the phone type the expressions using $\LaTeX$; however, I'm confident that the extra effort will be worthwhile.

 

[vel]

It's obvious that using a phone keyboard instead of a full-sized keyboard makes typing more cumbersome, and of course it's easier to post a screenshot of something previously hand-written and then photographed on your phone's camera than it is to on the phone type the expressions using $\LaTeX$; however, I'm confident that the extra effort will be worthwhile.

No, I mean I see all the code as plain text instead of it formatting. It's not that I couldn't type it on my phone, it's that I see the code itself, and it doesn't format at all. I'd like to be able to see my equations. Even your code for LaTeX shows up: I see exactly what you typed (the # symbols and \) instead of the way it's meant to be formatted.

 

[sysprog]

Does that still happen if you do a page refresh?

 

[vel]

Does that still happen if you do a page refresh?

Yes

 

[sysprog]

Also, what about this:

1) If the pipe is closed at the left end and open at the right end, determine the locations along the pipe (measured from the left end) of the displacement nodes for the first overtone.
2) If the pipe is closed at the left end and open at the right end, determine the locations along the pipe (measured from the left end) of the displacement nodes for the second overtone.

Questions 1) and 2) look to me to be exactly the same question, and it looks to me like there's insufficient information given $-$ what kind of scale? are the harmonics at octaves? well-tempered scale $-$ even-toned, etc..

 

[vel]

Also, what about this:

Questions 1) and 2) look to me to be exactly the same question, and it looks to me like there's insufficient information given $-$ what kind of scale? are the harmonics at octaves? well-tempered scale $-$ even-toned, etc..

I have no scale information given, sadly, but they're two different overtones. The first half of the problem was an open pipe, and I managed that fine, but what I've tried for this has been wrong. I don't have access to the question itself right now (the site crashed on me) but I have my work drawn out.
It's the same pipe, same length, but it's open and I had to find fundamental as well as third overtone displacement nodes

Fundamental: lambda = 1.8 * 2 = 3.6
Fundamental node: 1.8 / 2 = .9
1st: 1.8 / 4 = .45, (1.8 * 3) / 4 = 1.35
(so on and so forth following that pattern)

As I said, I've tried similar with one side closed and one side open, but my answers have been wrong

 

[Steve4Physics]

Homework Statement:: Standing sound waves are produced in a pipe that is 1.80 m long.
1) If the pipe is closed at the left end and open at the right end, determine the locations along the pipe (measured from the left end) of the displacement nodes for the first overtone.
2) If the pipe is closed at the left end and open at the right end, determine the locations along the pipe (measured from the left end) of the displacement nodes for the second overtone.
Relevant Equations:: (4 / 3) * L = lambda
1st overtone: L / 4, (3 * L) / 4
2nd overtone: L / 6, (3*L) / 6, (5 * L) / 6

(4 / 3) * (1.8) = 2.4 = lambda
1st overtone: 2.4 / 4 = .6; (2.4 * 3) / 4 = 1.8
View attachment 289163

Hi @vel. Please note:
Your working is difficult to read/follow.
You have thrown away marks by forgetting to include units.
You do not need to find frequency or wavelength (though you can if you want to do it the long/hard way!).
Your answers are incorrect.

On your drawing for Q1, clearly mark the tube length (1.8m) and mark the displacement node positions (‘N’). You should then be able to answer the question using only the diagram and primary school maths.

Post your updated drawing if you are still struggling.

Q2 is done the same way.

Edit. Both questions are about the same pipe - closed at the left end and open at the right end. Make sure that's correct.

 

[vel]

Hi @vel. Please note:
Your working is difficult to read/follow.
You have thrown away marks by forgetting to include units.
You do not need to find frequency or wavelength (though you can if you want to do it the long/hard way!).
Your answers are incorrect.

On your drawing for Q1, clearly mark the tube length (1.8m) and mark the displacement node positions (‘N’). You should then be able to answer the question using only the diagram and primary school maths.

Post your updated drawing if you are still struggling.

Q2 is done the same way.

Edit. Both questions are about the same pipe - closed at the left end and open at the right end. Make sure that's correct.

I have redrawn my diagram, but we've only done this sort of problem mathematically in class--I have no idea where the nodes should go, not even half-decent guesses. It's why I was trying to find the frequency and wavelength.

 

[sysprog]

Please excuse me, @vel, I didn't earlier notice that 2) refers to the second overtone while 1) refers to the first overtone $-$ I think that @Steve4Physics is right $\dots$

 

[Steve4Physics]

I have redrawn my diagram, but we've only done this sort of problem mathematically in class--I have no idea where the nodes should go, not even half-decent guesses. It's why I was trying to find the frequency and wavelength.
View attachment 289179

Node and antinodes on a standing wave are as shown here:
https://s3.amazonaws.com/bucketeer-...mages/000/001/166/original/02_.jpg?1591474020

Note that the distance between a node and an adjacent antinode is always 1/4 of a wavelength. So your diagram shows 3/4 of a wavelength = 1.8m. Can you now mark the nodes and work out the distances of the nodes from the left?

It sounds like you need to do a little bit of extra self-tuition. We normally first learn about standing waves/nodes/antinodes on a string. (And then move onto pipes). So try a video such as this one to help you with the basics.