How to Find Multiple Phase Constants

AI Thread Summary
To find multiple phase constants for a sinusoidal wave, one must understand the periodic nature of the sine function. The initial phase constant calculated was -0.151 rad, but other valid phase constants can be derived by adding or subtracting multiples of π (180 degrees). This is due to the sine wave's periodicity, where both the value and slope remain consistent across equivalent angles. Sketching the wave can help visualize these periodic properties and confirm the phase relationships. Understanding these principles allows for the identification of all possible phase constants effectively.
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Homework Statement


A sinusoidal wave traveling in the –x direction (to the left) has an amplitude of 20.0 cm, a wavelength of 35.0 cm and a frequency of 12.0 Hz. The transverse position of an element of the medium at t = 0, x = 0 is y = –3.00 cm and the element has a positive velocity here. (a) Sketch the wave at t = 0. (b) Find the angular wave number, period, angular frequency and wave speed of the wave. (c) Write an expression for the wave function y(x,t).

Homework Equations



y=Asin(kX-wt)

The Attempt at a Solution


[/B]
I solved for the phase constant by subbing in the initial values and found -0.151 rad. however, the solution said that there are other possible phase constants, such as π + 0.151 rad and 2π - 0.151rad, etc. I was wondering if someone could explain how to find the other phase constant values.

Thanks
 
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Hint: the sine wave is periodic.
 
Oh okay,

so would you just add or subtract 180 degrees to whatever phase constant you found?
 
A sine wave has the same overall phase if both the value and the slope are the same.
Use the periodicity of the sine wave you have, if you are uncertain then sketch out the first few periods and see - and put all angles in radians.
 
Thanks!
 
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