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Welcome to our Physics lesson on How to Obtain the Simplified Wave Equation from the General Equation of Waves, this is the second lesson of our suite of physics lessons covering the topic of General Equation of Waves, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
It is not always possible or suitable to use the general equation of waves as this requires information from many quantities. Also, this process involves complex calculations a user that is not very familiar with math may not understand. Therefore, it is more appropriate to use the simplified equation of waves
we already known from the previous tutorial in order to calculate any of the missing quantities contained in it. This situation is similar to when we used the simplified equation Fg = m × g for gravitational force instead of the long equation Fg = (G × m1 × m2) / r2.
But first, we must learn how to derive the simplified wave equation from the already confirmed equation of waves. Thus, given that we are discussing for waves whose form does not change in space and time, the argument is constant, i.e.
Taking the time derivative of the above expression, we obtain
Since
and
we obtain
In this way, we confirmed the simplified equation of waves
obtained in the previous tutorial.
Remark! The general and simplified equation of waves do not represent the same thing. The general equation of waves (in sine form) shown the fluctuations of the y-coordinate of any point of wave, i.e. how it moves up and down, while the simplified equation of waves shown how the wave propagates in space, i.e. how it moves horizontally. In few words, the equationis an equation of particles oscillation, while
is an equation of waves that carry energy, not particles.
In this regard, the equation v = λ × f is officially recognized as the equation of waves.
You have reached the end of Physics lesson 11.2.2 How to Obtain the Simplified Wave Equation from the General Equation of Waves. There are 3 lessons in this physics tutorial covering General Equation of Waves, you can access all the lessons from this tutorial below.
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