Worksheet: Phase Difference of Traveling Waves

In this worksheet, we will practice relating the phases of waves that have traveled different paths to the waves' properties and path lengths.

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?

  • AThe path lengths are equal.
  • BThe path lengths are 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?

  • ANo
  • BYes

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

  • ANo
  • BYes

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©?

  • A3.75Γ—10 m
  • B6.25Γ—10 m
  • C1.88Γ—10 m
  • D5.00Γ—10βˆ’6 m
  • E2.50Γ—10 m

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

  • A2.50Γ—10 m
  • B2.80Γ—10 m
  • C4.33Γ—10 m
  • D9.68Γ—10 m
  • E6.25Γ—10 m

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©?

  • A6.52Γ—10 s
  • B2.00Γ—10οŠͺ s
  • C2.37Γ—10 s
  • D1.12Γ—10οŠͺ s
  • E8.33Γ—10 s

Q4:

Plane electromagnetic waves with a wavelength of 480 nm are emitted from a point π‘ƒοŠ§, propagating through vacuum. The waves travel to the points π‘ƒοŠ¨ and π‘ƒοŠ©, as shown in the diagram. The displacement of π‘ƒοŠ¨ from π‘ƒοŠ§ is 1.22 ΞΌm and the displacement of π‘ƒοŠ© from π‘ƒοŠ§ is 1.06 ΞΌm. The waves emitted along both paths have the same initial phase.

What is the time difference between the waves arriving at π‘ƒοŠ¨ and at π‘ƒοŠ©?

  • A4.07Γ—10 s
  • B7.60Γ—10 s
  • C3.53Γ—10 s
  • D6.02Γ—10 s
  • E5.33Γ—10 s

How many wavelengths away from π‘ƒοŠ¨, along the line from π‘ƒοŠ§ to π‘ƒοŠ¨, are the waves from π‘ƒοŠ§ when the waves first arrive at π‘ƒοŠ©?

When the waves from π‘ƒοŠ§ first arrive at π‘ƒοŠ¨, what will the difference between their phase angle and the phase angle of the waves at π‘ƒοŠ© at the same instant be?

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