Two traveling waves g(x,t) = Asin(kx-wt) and h(x,t) = Asin(kx+wt+phi)

• blueberryRhyme
In summary, the figure does not include nodes or anti-nodes, but this is because it does not plot g+h. To find where the nodes must be, you have to identify a place where g+h is always zero. The statement of the problem may be one of multiple choices, and more information is needed to fully understand the context.
blueberryRhyme
Homework Statement
E. At particular values of t when troughs in one wave align with troughs in the other
Relevant Equations
N/A
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Last edited:
Where in the figure are there nodes at t1?

hutchphd
Hi haruspex, thank you for yr time to have a look at my question. the Figure doesn’t include nodes/anti nodes.

blueberryRhyme said:
Hi haruspex, thank you for yr time to have a look at my question. the Figure doesn’t include nodes/anti nodes.
That's only because the figure doesn't plot g+h. You can easily see where the nodes must be.

blueberryRhyme said:
You seem to have completely misunderstood the question.
You have to find a place where g+h is always zero.

The "statement" of the problem looks like one of the possible answers to a multiple choice question. If that is true, what is the question and what are the other choices?

1. What is the amplitude of the traveling waves?

The amplitude, represented by A, is the maximum displacement of the wave from its equilibrium position. In this case, both waves have the same amplitude, A.

2. What do k and w represent in the equations?

k is the wave number, which is equal to 2π divided by the wavelength. It represents the number of complete cycles of the wave per unit distance. w is the angular frequency, which is equal to 2π divided by the period. It represents the speed at which the wave oscillates.

3. How do the two waves differ from each other?

The main difference between the two waves is the phase shift, represented by phi. In the first wave, g(x,t), the phase shift is 0, while in the second wave, h(x,t), the phase shift is phi. This results in the two waves having different positions at any given time, even though they have the same amplitude and frequency.

4. What is the relationship between the two waves?

The two waves are called traveling waves because they both move in the same direction with the same speed and frequency. They are also considered to be in phase with each other, meaning they have the same starting point and are in sync with each other as they move.

5. How can these equations be used in real-life applications?

These equations are commonly used in the study of wave phenomena, such as sound waves, light waves, and water waves. They can also be applied in fields such as acoustics, optics, and oceanography to model and analyze various wave behaviors and interactions.

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