The following figure shows wave A (solid line), and wave B
(dotted line).
1.
What is the starting phase of wave A? 270°
2.
What is the starting phase of wave B? 0°
3.
What is the starting phase difference (A-B) between the two waves?
270°
Note: To obtain this, you start at 270°, and go clockwise in the circle
till you get to 0°. You’ve traveled 270° in terms of the circle.
4.
What is the instantaneous phase of wave A at time 0.25 s? 90°
5.
What is the instantaneous phase of wave B at time 0.25 s? 180°
6.
What is the instantaneous phase difference (A-B) between the two waves
at time 0.25 s? 270°
Note: To obtain this, you start at 90°, and go clockwise in the circle
till you get to 180°. You’ve traveled 270° in terms of the circle. It is
very important to identify your starting point, and stick to the same
direction (clockwise or anticlockwise) in your circle. If not, you’ll get
an answer of 90°.
Use the circle to verify your answers
90°
0°
180°
270°
1.
What is the instantaneous phase difference (A-B) between the two
waves at time 0.5 s?
Instantaneous phases of A and B are 270° and 360°, respectively.
The difference between them is 270°. Note that this answer will
become 90° if you start at 360° instead of 270°, and travel in the
anticlockwise direction.
z
Are the two phase differences (Questions 6 and
If not, explain why you obtained different values.
7) the same?
They should be the same as the two waves have the same
frequency. However, you will get different values if you switch
starting points and directions.
The following figure shows wave A (solid line), and wave B
(dotted line).
1. What is the starting phase of wave A? 0°
2. What is the starting phase of wave B? 90°
3. What is the starting phase difference (A-B) between the two waves?
270° if you travel in the clockwise direction and start from A.
4. What is the instantaneous phase of wave A at time 0.005 s? 360°
5. What is the instantaneous phase of wave B at time 0.005 s? 270°
6. What is the instantaneous phase difference (A-B) between the two waves at time
0.005 s?
90° if you stick to the same direction and start from A.
7. What is the instantaneous phase difference (A-B) between the two waves at time
0.0175 s (Halfway between times 0.015 and 0.02 s)?
180° - 360°, difference is 180°
8. What is the instantaneous phase difference (A-B) between the two waves at time
0.05 s?
360° - 90°, difference is 270°
9. Are the three phase differences (Questions 6, 7, and 8) the same? If not, explain
why you obtained different values.
The values are different because the frequencies are different.