How Do You Calculate the Phase Constant φ from a Wave Displacement Graph?

[jhans11]

1. The figure shows the displacement y versus time t of the point on a string at x = 0, as a wave passes through that point. The scale of the x axis is set by ys = 18.0 mm.The wave has form y(x, t) = ym sin (kx - ωt+φ). What is φ?
http://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c16/pict_16_62.gif2. y(x, t) = ym sin (- ωt+φ)3. reading off my graph, it crosses the Y axis at 6mm, i used that as my Y(x,t) and 18 as my Ym, but i have no idea how to get the time or omega

 

[Spinnor]

Your graph did not display.

 

[jhans11]

Your graph did not display.

http://imgur.com/svRs4Uq

 

[andrevdh]

At t = 0 seconds the displacement is +6 mm and you have y_m.

 

[HalfLostAndSearching]

I would first suggest checking the given equation for any errors or missing information. The equation should include a value for the wave number (k) and the angular frequency (ω). Without these values, it is not possible to accurately determine the phase constant (φ).

If the equation is correct and complete, then the best way to determine φ would be to use the given information about the displacement and the scale of the x axis. From the graph, it appears that the displacement at x = 0 is 6mm, and the maximum displacement (Ym) is 18mm. Using these values, we can rearrange the equation to solve for φ as follows:

φ = -arcsin(6/18) = -30°

However, it is important to note that this calculation assumes that the wave is a simple sinusoidal wave and does not take into account any complex or non-linear behavior. It would be best to confirm this result by comparing it to other points on the graph or by using a more accurate measurement method. Additionally, if the wave is more complex, it may be necessary to use a more advanced mathematical approach to accurately determine the phase constant.