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 unequal.
  • BThe path lengths are equal.

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

  • ANo
  • BYes

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

  • ANo
  • BYes

Q2:

Electromagnetic waves with a wavelength of 625 nm are emitted from a point 𝑃  . The initial displacement at 𝑃  is zero, which increases positively. The waves travel to the point 𝑃  , 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 𝑃  to 𝑃  is drawn to scale with the wavelength of the waves emitted from 𝑃  . The graph shows the change in displacement of the wave with time at the point 𝑃  , starting from the instant at which the displacement at 𝑃  starts to change, before which it has a constant value of zero. At the instant that waves start to emit from 𝑃  , waves with the same amplitude, wavelength, and phase are emitted from the point 𝑃  .

What is the length of the line from 𝑃  to 𝑃  ?

  • A 6 . 2 5 Γ— 1 0   m
  • B 5 . 0 0 Γ— 1 0 βˆ’ 6 m
  • C 1 . 8 8 Γ— 1 0   m
  • D 2 . 5 0 Γ— 1 0   m
  • E 3 . 7 5 Γ— 1 0   m

What is the length of the line from 𝑃  to 𝑃  ?

  • A 4 . 3 3 Γ— 1 0   m
  • B 6 . 2 5 Γ— 1 0   m
  • C 2 . 5 0 Γ— 1 0   m
  • D 9 . 6 8 Γ— 1 0   m
  • E 2 . 8 0 Γ— 1 0   m

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