- #1
songoku
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- 335
- Homework Statement
- This is not homework
I want to ask about equation of traveling wave. I read in my book the derivation of equation of traveling wave. The explanation starts from equation ##y=A \sin (kx)## then change into ##y=A \sin (kx - \omega t)## as the wave moves to the right. If the wave moves to the left, the term inside the sin would be ##(kx + \omega t)##
- Relevant Equations
- ##y=A \sin (kx + \omega t)##
##y=A \sin (-kx - \omega t)##
But in the notes from teacher, the equation is ##y=A \sin (kx - \omega t)## for wave traveling to the right and ##y=A \sin (-kx - \omega t)## for wave traveling to the left
When I transform the equation of the wave traveling to the left using trigonometry:
$$y=A \sin (-kx - \omega t)$$
$$y=-A \sin (kx + \omega t)$$
The issue is in the practice question, there is question asking the initial direction of movement of the wave, will it move upwards or downwards. Equation ##y=A \sin (kx + \omega t)## states that the wave initially moves upwards but ##y=-A \sin (kx + \omega t)## states the wave moves downwards initially. It means that the answer to the question will differ, depends on which equation I use.
In this youtube video,
()
There is another equation for wave traveling to the right, which is ##y=A \sin (\omega t - kx)## which is equal to ##y=-A \sin (kx - \omega t)##. This means that the initial vertical movement for wave traveling to the right will differ from two previous equations.
How to address the difference? Thanks
When I transform the equation of the wave traveling to the left using trigonometry:
$$y=A \sin (-kx - \omega t)$$
$$y=-A \sin (kx + \omega t)$$
The issue is in the practice question, there is question asking the initial direction of movement of the wave, will it move upwards or downwards. Equation ##y=A \sin (kx + \omega t)## states that the wave initially moves upwards but ##y=-A \sin (kx + \omega t)## states the wave moves downwards initially. It means that the answer to the question will differ, depends on which equation I use.
In this youtube video,
()
There is another equation for wave traveling to the right, which is ##y=A \sin (\omega t - kx)## which is equal to ##y=-A \sin (kx - \omega t)##. This means that the initial vertical movement for wave traveling to the right will differ from two previous equations.
How to address the difference? Thanks