11.2.2 Interference

Question 1

Interference

Answer 1

• When two sinusoidal traveling waves of the same frequency interfere, the result is another sinusoidal traveling wave of the same frequency.
• Depending on the phase difference between them, two sinusoidal traveling waves of the same frequency can interfere:
- totally constructively, resulting in a wave of large amplitude,
- totally destructively, resulting in a flat wave with zero amplitude, or
- partially constructively or destructively.

Question 2

Two identical traveling sine waves interfere constructively if the phase difference theta between them is 0. For which of the following phase differences will the two waves interfere constructively?

Answer 2

All of the above

Question 3

Suppose the phase of Wave 1 is 0 and the phase of Wave 2 is pi. Which of the following is the lag time between the two waves? Assume all the other parameters are the same for both waves

Answer 3

• pi/w
• 1/2f
• 1/2*T, where T is the frequency

Question 4

If two traveling sine waves cancel each other, or interfere destructively, what is the phase difference between the two waves?

Answer 4

theta = pi

Question 5

Two sine waves are traveling to the right on a rope with a phase difference of pi/2. Mathematically, which of the following expressions is the sum of the two waves? Assume both waves have the same frequency, wavelength, and amplitude.

Answer 5

2A/sqrt(2) cos(kx - wt)

Question 6

Two sine waves are traveling in phase to the right on a rope. The amplitude of one wave is A, while the amplitude of the second wave is ½ A. Both waves have the same frequency and wavelength. Mathematically, which of the following expressions is the sum of the two waves?

Answer 6

3A/2 cos(kx - wt)

Question 7

Evaluate the following as true or false. Consider a traveling sine wave given by y(x, t) = A cos (kx - wt + theta). The phase theta is independent of the frequency and wavelength. It depends only on the initial conditions

Answer 7

true

Question 8

Evaluate the following as true or false. Two sine waves are traveling to the right with phase difference theta. The interference pattern generated by the two waves does not depend on the phase difference.

Answer 8

false

Question 9

Two sine waves with equal w, k, and A (amplitude) are traveling to the right on a rope. Which of the following phase differences between the two waves will generate a wave with the same amplitude A ?

Answer 9

theta = 2pi/3

Question 10

Tow sine waves with equal w, k, and A (amplitude) are traveling to the right on a rope. The two waves have a phased difference theta, therefore y1 = A cos(kx - wt) and y2 = A cos(kx - wt + theta). What is their sum?

Answer 10

2A cos (theta/2) cos (kx - wt + theta/2)