What Is the Initial Phase Angle Beta in Wave Propagation?

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Homework Help Overview

The discussion revolves around determining the initial phase angle beta in the context of wave propagation along a string. The problem involves a specific wave equation and parameters related to the wave's characteristics, including amplitude, angular frequency, and wave number.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the wave equation and its derivatives to find the phase angle. There is a mention of an attempt to solve for beta using the transverse speed and the wave equation, but the result was questioned.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to calculate beta. One participant has provided an attempt but received feedback suggesting a review of their calculations, particularly regarding signs in the derivative.

Contextual Notes

There is an assumption that the phase angle beta must fall within a specific range, which is part of the problem's constraints. The discussion also highlights potential issues with the application of the derivative in the context of the wave equation.

efairall
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A wave is propagating down a string having a diameter of 0.0013 m and a density of
5240 kg/m3. The wave has the form y = A sin(k x - w t + beta)
where A = 0.011 m, w = 59.8 rad/s, and k = 72.4 rad/m.
the velocity of propagation of the wave is 0.825967 m/s

The transverse speed @ y/@t is 0.177606 m/s at x = 0.0102762 m and t = 0.00385686 s.
What is the initial phase angle beta if we assume that 0 < k x - w t + beta < pi ?
Answer in units of rad.
 
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What have you attempted so far towards solving this?
 
i have used the formula.. zy/zt =wAcos((kx - wt + (beta))
and solved for beta. i got an answer 0.78 and it was wrong.
 
Double-check your +/- signs, what's the derivative of -wt?

You're on the right track.
 

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