What is the relationship between A and B in the given equation?

In summary, the conversation discusses a problem involving the relationship between two functions A and B, represented by the equation E = [axhat(A(x+y)) = ayhat(B(x-y))]cos(wt). The individual attempting to solve the problem has expanded the equation and reduced it to a simpler form, but is unsure of the next steps. They mention the possibility of manipulating the cosine component and converting to the frequency domain, and also suggest considering the equation in the context of a wave equation or electric field with additional conditions. However, they also note that the rearrangement they made may be incorrect since A(x+y) and B(x-y) may be functions of those arguments.
  • #1
PassThePi
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0

Homework Statement


E = [axhat(A(x+y)) = ayhat(B(x-y))]cos(wt)

Determine the relationship between A and B

Homework Equations


I don't know if there are any.

The Attempt at a Solution


I've expanded the problem and reduced it to E = cos(wt)[x(A+B)axhat + y(A-B)ayhat]
I was going to take the real component and convert to the frequency domain to try to manipulate the cosines but I don't know if that's the right step.

If someone could just get me started or point me in the right direction I think I could figure it out. Not looking for someone to do this for me.
 
Last edited:
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  • #2
It would help to know what E represents. Is it supposed to be a solution to the wave equation or some other pde? If so, you can try to apply that equation and find conditions on A and B. If E is an electric field, there is an additional condition on its divergence that might be useful.

Also, it seems likely that A(x+y) and B(x-y) are meant to be functions of those arguments, so the rearrangement that you made is probably incorrect.
 

Related to What is the relationship between A and B in the given equation?

1. What is the definition of "Relationship between A and B"?

The relationship between A and B refers to the connection or association between two variables, factors, or entities. It can be a causal or correlative relationship, where one variable affects the other or they are simply related in some way.

2. How do you determine the strength of the relationship between A and B?

The strength of the relationship between A and B can be determined by calculating the correlation coefficient, which measures the degree of linear relationship between two variables. It ranges from -1 to +1, where a value closer to +1 indicates a strong positive relationship, while a value closer to -1 indicates a strong negative relationship.

3. Can you give an example of a positive relationship between A and B?

An example of a positive relationship between A and B is the relationship between studying and grades. As the amount of time spent studying (variable A) increases, the grades (variable B) also tend to increase. This shows a positive correlation between the two variables.

4. Is there always a cause-and-effect relationship between A and B?

No, there is not always a cause-and-effect relationship between A and B. Sometimes, two variables may be related without one causing the other. This is known as a correlation, where the variables change together but one does not necessarily cause the other.

5. How can understanding the relationship between A and B be useful?

Understanding the relationship between A and B can be useful in various fields, such as social sciences, business, and healthcare. It can help identify patterns and trends, make predictions, and inform decision-making. It can also aid in understanding the mechanisms behind certain phenomena and guide further research.

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