Answer to Question #280289 in Physics for Ahmad

Question

Given the wavefunction of a standing wave: y(x,t) = A sin(πx)cos(2πt), where x and y are in meters and t is in seconds. The position of the second anti-node from the end x = 0 is at:

Answer 1

Given:

$y(x,t) = A \sin(πx)\cos(2πt)$

The positions of anti-nodes are given by the equation

$$\sin(\pi x)=\pm 1$$

So

$$\pi x=\pi/2+\pi n, \quad n=0,1,2,...\\ x=1/2+n$$

The position of second anti-node from origin

$$x=1/2+1=3/2\:\rm m=1.5\: m$$