What is the Coordinate of Point B in a Sinusoidal Wave?

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Homework Help Overview

The discussion revolves around determining the coordinate of point B in a sinusoidal wave, specifically where it is 60.0° out of phase with point A, which is located at the origin. The wave function provided is a cosine function, and participants are exploring the implications of phase differences in the context of wave mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between phase and position along the x-axis, considering the wave's properties and the constant time condition. There is an attempt to express the phase difference mathematically and to relate it to the x-coordinate of point B.

Discussion Status

The conversation is ongoing, with participants providing insights into the phase relationship and questioning calculations. Some guidance has been offered regarding the interpretation of the phase change, but no consensus has been reached on the exact coordinate of point B.

Contextual Notes

Participants note the constraints of the problem, including the requirement to analyze the wave at a specific instant and the lack of an accompanying image to clarify the wave's characteristics.

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Homework Statement



Consider the sinusoidal wave in the figure, with the wave function below.

At a certain instant, let point A be at the origin and point B be the first point along the x-axis where the wave is 60.0° out of phase with point A. What is the coordinate of point B?

y = (15.0 cm) cos(0.157x - 50.3t)

and I am not allowed to post the image but here's some helpful information:
its a cosine graph, and \lambda = 40 cm, T = 0.125 s, f = 8.00 hz, k = 0.157 rads/cm

Homework Equations



Some equations that I have are:
k=2\pi/\lambda
v=\lambda*f
y=Asin(kx-\omegat)

The Attempt at a Solution


What I have tried so far is:
y=15*sin((.157)x-(50.3)t + \pi/3)
The example says " The vertical position of an element of the medium at t = 0 and x = 0 is also 15.0 cm "
The only problem is that I am really stuck and I cannot seem what to set the 60.0\circ equal to. Help would be much appreciated! Thank you!
 
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Everything in the argument of the cosine is the phase of the wave. So the phase is a function of both x and t. However, we're looking at this wave at a particular "instant", which means that t is constant. So, the only thing that would cause a phase change is x. So how far from the origin would the x coordinate of point B have to be in order for 0.157x - 50.3t to differ from 0.157*(0) - 50.3t by 60 degrees, given that t is constant?
 
Would x = 6.37 * \pi because that would make it (\pi/3 -50.3t)
 
I think you might be off by a factor of 3. Check your work again.
 

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