Standing Waves in Strings: Examining Amplitude, Node Number, and Wave Speed

[BMWPower06]

Homework Statement

The figures below show systems of standing waves set up in strings, fixed at both ends, under tension. All of the strings are under the SAME tension and are otherwise identical, EXCEPT for their lengths. The variables in these situations, in addition to the lengths (L) of the strings, are the amplitudes (A) at the antinodes and the number of nodes in the standing wave.

http://aycu10.webshots.com/image/21209/2002759293776541254_rs.jpg

Which of the following statements are true about the situations depicted in the figures above?

True False The wave speed does not depend on the amplitude of the wave
True False Figure E has a wavelength of 20 cm
True False Figure B has the most nodes
True False All of the standing wave patterns have the same wave speed
True False Figures C and F have the same frequency

The Attempt at a Solution

I looked through my book, and i know that I am close, I am just not sure which ones are wrong. My answers are in bold, and the computer says its wrong, but not which ones are wrong. Any help?

Thanks

 

[Doc Al]

Which ones are you unsure of? What is your reasoning behind your answers?

 

[BMWPower06]

Which ones are you unsure of? What is your reasoning behind your answers?

Well:
1) V= Sqrt T/U so i think that's right
2) Wavelength is from one antinode to another, so i think that is right
3) Figure B has the most frequency so it has the most nodes
4) Not too sure about this one
5) They both have 3 occurences in the same period so they must be the same

I don't know which is wrong, i tried changing number 4 but that was still wrong.

 

[Doc Al]

Well:
1) V= Sqrt T/U so i think that's right

OK

2) Wavelength is from one antinode to another, so i think that is right

From one antinode to the next is a half wavelength, but OK.

3) Figure B has the most frequency so it has the most nodes

You can just count the nodes.

4) Not too sure about this one

What does wave speed depend on?

5) They both have 3 occurences in the same period so they must be the same

Why do you think the period is the same?

 

[BMWPower06]

OK

From one antinode to the next is a half wavelength, but OK.

You can just count the nodes.

What does wave speed depend on?

Why do you think the period is the same?

4. length and tension/force

5. because they are all in the same window, but I am not too sure

 

[Doc Al]

4. length and tension/force

Wave speed does not depend on length. Review the formula that you quoted regarding question 1.

5. because they are all in the same window, but I am not too sure

The windows are not all the same size. Check the length of each window, which is labeled on the diagram.