# 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 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 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

**Q3: **

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

- A s
- B s
- C s
- D s
- E s

**Q4: **

Plane electromagnetic waves with a wavelength of 480 nm are emitted from a point , propagating through vacuum. The waves travel to the points and , as shown in the diagram. The displacement of from is 1.22 ΞΌm and the displacement of from 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 and at ?

- A s
- B s
- C s
- D s
- E s

How many wavelengths away from , along the line from to , are the waves from when the waves first arrive at ?

When the waves from first arrive at , what will the difference between their phase angle and the phase angle of the waves at at the same instant be?