Two sinusoidal waves traveling in opposite directions interfere to produce a standing wave described by the wave function

where x and y are in meters and t is in
seconds.

a. What is the amplitude of one of the interfering waves?

b. Find the second smallest value of the position x corresponding to an antinode.

c. Find the third smallest value of the position x corresponding to a node.

Example
1

a. The amplitude = m

a. In the case of standing waves, the resultant wave is given by

where y_{m} is
the amplitude of the two interfering waves. Therefore, the two interfering
waves have equal amplitudes of (2.5 m) /2 = 1.25 m each.

Answer

b.
Antinodes are positions of *
maximum displacement* and given by

In this case the wavelength is

The second smallest value of x corresponding to an antinode is for n = 1,
which gives x_{2} =
3.9 m.

b. The second antinode is at x = m

c.
Nodes are positions of *zero
displacement* and given by

The third
smallest value of x corresponding to a node is for n = 2, that is x_{3 }=
5.2 m.

b.The third node is at x = m