Where is the maximum speed of a vibrating string?

[msimard8]

The figure shown here represents a spring vibrating at its second overtone. The points labeled (A), (B), and (C) represent the central point of the string at various times.

a) At which location is the central point of the string moving at its maximum speed.

b) A t which locating is it instantaneous speed zero?

c) At which location is the point on the string moving with an intermediate speed?



oK Its kinda hard to show this on a forum but take a look

here is one loop of he wave


/--------A-------\
/--------------------\
|----------C-----------|center of wave (string)
\----------B---------/
\-------------------/

I don't know how well you would understand this but picture that as a standing wave.

Anyway for part A, my guess would be the maxium speed is would be A. I can't explain a reasoning though.

Part B wouuld be zero because that is the level of the nodes that do not move at all.

part c: Would be B becasue it is inbetween A and C.


I don't understand the reasoning why A is the max speed, if it is the max speed. Maybe A is not the max speed because that is the point where it swithces directions and has to stop.

Help

 

[lightgrav]

If A is as far from the "straight string" location as this point gets,
then A would be where it turns around, where its speed is zero.
You can think of EACH piece of string as oscillating around its equilibrium location.
An oscillator has the most Potential Energy at its two extreme displacements from equilibrium. We usually consider the PE zero AT the equilibrium location. The other kind of Energy contained in an oscillator is Kinetic.

Where is KE maximum? Where is it zero?

 

[msimard8]

so i still don't quite understand

At point A, the speed is 0 because it is turning around


At point B its inbetween 0 and max speed because it is not going its fastest, nor its slowest. There fore it is intermideate

At point C, it is going the max speed. Why? Isnt it at the level of nodes, which don't move at all.

 

[msimard8]

help


it still don't make sense

 

[jackie48]

the max speed is given by the max displacement (the part of the strings strings furthest position from equilibrium) because at the pont of max displacement the string has the most potential energy. don't know how else to explain it, it's pretty simple.