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
Dick said:Tell me what 'node' means.
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
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
The x>0 in the standing wave equation refers to the position along the wave where the amplitude is measured. This means that only the points on the positive side of the x-axis are considered in the equation.
The standing wave equation is derived from the general wave equation, which describes the behavior of waves in a medium. The standing wave equation is a special case of this equation, where the wave is confined within a specific space and does not travel.
The nodes in the standing wave equation represent points along the wave where the amplitude is zero. These points occur at regular intervals and are important for understanding the behavior and properties of standing waves.
The number of nodes in a standing wave is directly related to its frequency. As the number of nodes increases, the frequency of the wave also increases. This means that waves with more nodes have a higher pitch and shorter wavelength.
The restriction of x>0 in the standing wave equation is important because it allows us to accurately describe the behavior of standing waves in a specific space. Without this restriction, the equation would not accurately represent the behavior of standing waves and could lead to incorrect conclusions.