Lesson: Phase Difference of Traveling Waves

Physics

In this lesson, we will learn how to relate the phases of waves that have traveled different paths to the waves’ properties and path lengths.

Worksheet

Q1:

Two electromagnetic waves propagate past a line 𝐿. The paths of the electromagnetic waves intersect at a point on a line 𝐿, as shown in the diagram. The points of zero displacement of each wave are shown by lines perpendicular to the directions of the paths of the waves’ propagation. The longer-wavelength electromagnetic wave has a wavelength double that of the shorter-wavelength electromagnetic wave.

Are the path lengths of the two rays in the region between 𝐿 and 𝐿 equal or unequal?

Do the phases of the waves at the point where their paths intersect each other differ by an integer multiple of 2πœ‹ radians?

Do the phases of the waves at the point where their paths intersect 𝐿 differ by an integer multiple of 2πœ‹ radians?

Q2:

Electromagnetic waves with a wavelength of 625 nm are emitted from a point π‘ƒοŠ§. The initial displacement at π‘ƒοŠ§ is zero, which increases positively. The waves travel to the point π‘ƒοŠ©, as shown in the diagram. The lengths of the sides of the triangle in the diagram are not to scale with each other, but the line from π‘ƒοŠ§ to π‘ƒοŠ© is drawn to scale with the wavelength of the waves emitted from π‘ƒοŠ§. The graph shows the change in displacement of the wave with time at the point π‘ƒοŠ©, starting from the instant at which the displacement at π‘ƒοŠ© starts to change, before which it has a constant value of zero. At the instant that waves start to emit from π‘ƒοŠ§, waves with the same amplitude, wavelength, and phase are emitted from the point π‘ƒοŠ¨.

What is the length of the line from π‘ƒοŠ¨ to π‘ƒοŠ©?

What is the length of the line from π‘ƒοŠ¨ to π‘ƒοŠ§?

Q3:

Plane electromagnetic waves are emitted from the points π‘ƒοŠ§ and π‘ƒοŠ¨, toward a point π‘ƒοŠ©, propagating through vacuum. The displacement of π‘ƒοŠ© from π‘ƒοŠ§ is 3.36 Β΅m and the displacement of π‘ƒοŠ© from π‘ƒοŠ¨ is 2.65 ΞΌm. The waves from π‘ƒοŠ§ and π‘ƒοŠ¨ are in phase with each other at π‘ƒοŠ©. How much time after the waves from π‘ƒοŠ¨ arrive at π‘ƒοŠ© do the waves from π‘ƒοŠ§ arrive at π‘ƒοŠ©?

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