1-11 Standing Waves

Two waves are propagating on the same very long string. A generator at one end of the string creates a wave given by

and another generator at the other end creates the wave given by

 

a. Find the position of the first node.

b. Find the position of the second antinode

a. The first node is at x = m.

a. The resultant wave is

 

We need to use the trigonometric formula

 

where

b.   The antinodes have maximum amplitude.

 

 

  The second antinode is located at x = 1.0 m.

b. The second antinode is at  x = m

 

 

 

 The nodes have zero amplitude.

 

 

 

 

 Therefore, the first node is located at x = 0.50 m.