11.3.1 Standing Waves: Two Waves Traveling in Opposite Directions

Question 1

Standing Waves: Two Waves Traveling in Opposite Directions

Answer 1

• When two sinusoidal traveling waves of the same frequency moving in opposite directions interfere, the result is called a standing wave. Standing waves do not propagate through space; instead, the medium moves in such a way that some points,called nodes, remain motionless.
• Although they do not transport energy, standing waves do contain energy. This energy changes forms from potential to kinetic and back again, much like the energy of a simple harmonic oscillator.

Question 2

A standing wave is described by the equation y (x, t) = 2 A sin k x cos ω t. The position along a wave depends on which of the following parameters?

Answer 2

Wavelength ( λ)

Question 3

True or false?

Along a standing wave, the maximum amplitude of each point depends on its location.

Answer 3

true

Question 4

The maximum displacement of a standing wave is 0.2 m. Assume this standing wave is generated as a result of two interfering waves of equal amplitude, frequency, and wavelength. Which of the following is the amplitude of each of the two interfering waves?

Answer 4

0.1 m

Question 5

Two waves, y1 = A sin(kx + wt) and y2 = Asin(kx - wt), cross each other and interfere. In which directions are they moving?

Answer 5

Wave y1 moves to the left while y2 moves to the right

Question 6

Two sine waves moving in opposite directions interfere to generate standing waves. If y1 = A sin(kx + wt) and y2 = Asin(kx - wt), then the resultant wave y1 + y2 is equivalent, to which of the following expressions?

Answer 6

y = 2 A sin kx cos wt

Question 7

Except for the nodes on a standing wave, what is the frequency f of the points executing simple harmonic motion?

Answer 7

f = w/2pi