Understanding phase difference

In summary, the conversation discusses two waves with identical frequency but different amplitudes occupying the same region of space. The question is at what phase difference does the resulting wave have the largest amplitude, and the formula for calculating this is given. The solution is that the resultant amplitude is maximum when the phase difference is a multiple of 2*pi. The person requesting help thanks the responder for their assistance.
  • #1
kavamo
45
0

Homework Statement



Two waves with identical frequency but different amplitudes A1 = 6.0 cm and A2 = 2.0 cm, occupy the same region of space (are superimposed).

(a) At what phase difference does the resulting wave have the largest amplitude?

Homework Equations



I have found the amplitude of the resulting wave (8.0 cm) which was the second part of the problem) but am not sure how to calculate the phase difference. The formula in my books is:

d1-d2/lamda(wavelength)

The Attempt at a Solution



The problem is I don't know/understand how to solve for the distances. Can anyone point me in the right direction?

Thanks.
 
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  • #2
Resultant amplitude is maximum when the phase difference is 2*n*pi, where n = 0, 1, 2, ..etc.
 
  • #3
Thank you for the assist.

kavamo
 

1. What is phase difference?

Phase difference is a measure of how two waves are shifted relative to each other in terms of their peaks and troughs. It is usually expressed in radians or degrees and can have a value between 0 and 2π.

2. How is phase difference related to frequency?

The phase difference between two waves is directly related to their frequencies. As the frequency increases, the phase difference also increases. This means that waves with higher frequencies have a larger phase difference between them compared to waves with lower frequencies.

3. What is the significance of phase difference in wave interference?

Phase difference plays a crucial role in determining the type of interference that occurs between two waves. When the phase difference is 0, the waves are said to be in phase and constructive interference occurs. When the phase difference is 180°, the waves are said to be out of phase and destructive interference occurs.

4. How is phase difference measured?

Phase difference can be measured using a variety of methods, including using an oscilloscope or a phase meter. These instruments measure the difference in time between corresponding points on the two waves and convert it to a phase difference value.

5. What are some real-world applications of understanding phase difference?

Understanding phase difference is important in various fields such as engineering, acoustics, and optics. It is used in designing electronic circuits, controlling sound systems, and analyzing the properties of light. It is also crucial in fields like astronomy for studying the behavior of celestial bodies.

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