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

[Outrageous]

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

 

[Dick]

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.

 

[Outrageous]

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

 

[Dick]

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.

 

[Outrageous]

Yup, y=0, thank you very much

 

[Outrageous]

Then for antinode position is dy/dT= 0 ? The amplitude is maximum for all kind of y.

 

[Outrageous]

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

 

[Dick]

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.

 

[Outrageous]

Why I can't use dy/dT=0? Is that because x<0? What does that mean ? please .