What is the x>0 mean here? standing wave equation find nodes?

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Homework Help Overview

The discussion revolves around the standing wave equation given by y = 2sin(31.42x)cos(7854t) and the task of finding the positions of the first two nodes for x > 0. Participants are exploring the implications of the equation and the definitions of nodes and antinodes in the context of standing waves.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants question the initial conditions of the standing wave, such as whether it starts from a node or an antinode. There is uncertainty about the meaning of 'node' and how to calculate positions without clear parameters for x. Some participants attempt to define nodes and antinodes, while others explore the implications of the conditions x > 0 and x < 0.

Discussion Status

There is an ongoing exploration of definitions and conditions related to nodes and antinodes. Some participants have provided clarifications about the nature of nodes, while others are still seeking to understand how to apply these concepts to find the required positions. Multiple interpretations of the problem are being discussed, particularly regarding the constraints on x.

Contextual Notes

Participants note the lack of information regarding the length of x and the initial conditions of the standing wave. The distinction between nodes and antinodes is also under examination, with some confusion about the implications of the conditions x > 0 and x < 0.

Outrageous
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Homework Statement


Two waves travel in opposite direction form a standing wave of y= 2sin(31.42x)cos(7854t).
Find the positions of first two nodes with x>0.


Homework Equations





The Attempt at a Solution


The question didn't say whether the standing wave starts from node or antinode . The question didn't say how long is x, even I know the wavelength and frequency also don't know how to calculate, how? Please help
 
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Outrageous said:

Homework Statement


Two waves travel in opposite direction form a standing wave of y= 2sin(31.42x)cos(7854t).
Find the positions of first two nodes with x>0.


Homework Equations





The Attempt at a Solution


The question didn't say whether the standing wave starts from node or antinode . The question didn't say how long is x, even I know the wavelength and frequency also don't know how to calculate, how? Please help

Tell me what 'node' means.
 
Dick said:
Tell me what 'node' means.

The point that is not moving in standing wave. X=0. Then t= 0 ,then I will get first node, the second node, t=2?

Thanks
 
Outrageous said:
The point that is not moving in standing wave. X=0. Then t= 0 ,then I will get first node, the second node, t=2?

Thanks

No, a node is a point where y=0 for all values of t. Try to find the first two value of x that satisfy 2sin(31.42x)=0.
 
Yup, y=0, thank you very much
 
Then for antinode position is dy/dT= 0 ? The amplitude is maximum for all kind of y.
 
The position of the first two antinode s with x< 0. X<0 here mean they want the x value be negative , if I use, dy/dt = 0, then I will get sin34.42x= 0 , how to make x become less than zero here? Please thanks
 
Outrageous said:
The position of the first two antinode s with x< 0. X<0 here mean they want the x value be negative , if I use, dy/dt = 0, then I will get sin34.42x= 0 , how to make x become less than zero here? Please thanks

Antinode is where the amplitude reaches a maximum as a function of x. To find maxima you want to use calculus and solve dy/dx=0.
 
Why I can't use dy/dT=0? Is that because x<0? What does that mean ? please .
 

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