Physics Lesson 11.2.2 - How to Obtain the Simplified Wave Equation from the General Equation of Waves

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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.

How to Obtain the Simplified Wave Equation from the General Equation of Waves?

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

v = λ × f

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.

k × x - ω × t = constant

Taking the time derivative of the above expression, we obtain

k × dx/dt - ω = 0
k × v - ω = 0
k × v = ω
v = ω/k

Since

ω = /T
= 2π × f

and

k = /λ

we obtain

v = (/T)/(/λ)
= λ/T
= λ × f

In this way, we confirmed the simplified equation of waves

v = λ × f

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 equation

y(x,t) = ymax × sin(k × x - ω × t + φ)

is an equation of particles oscillation, while

v = λ × f

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.

More General Equation of Waves Lessons and Learning Resources

Waves Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
11.2General Equation of Waves
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
11.2.1Wave Function. General Equation of Waves
11.2.2How to Obtain the Simplified Wave Equation from the General Equation of Waves
11.2.3Speed and Acceleration of Oscillating Particles in a Wave

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  2. Waves Physics tutorial: General Equation of Waves. Read the General Equation of Waves physics tutorial and build your physics knowledge of Waves
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  5. Check your calculations for Waves questions with our excellent Waves calculators which contain full equations and calculations clearly displayed line by line. See the Waves Calculators by iCalculator™ below.
  6. Continuing learning waves - read our next physics tutorial: Energy and Power of Waves

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