# 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 . The paths of the electromagnetic waves intersect at a point on a line , 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 wavesβ 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 and 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 radians?

- ANo
- BYes

Do the phases of the waves at the point where their paths intersect differ by an integer multiple of radians?

- ANo
- BYes

**Q2: **

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

What is the length of the line from to ?

- A m
- B m
- C m
- D m
- E m

What is the length of the line from to ?

- A m
- B m
- C m
- D m
- E m