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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

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*

k × v - ω = 0

k × v = ω

v =

Since

ω = *2π**/**T*

= 2π × f

= 2π × f

and

k = *2π**/**λ*

we obtain

v = (*2π**/**T*)/(*2π**/**λ*)

=*λ**/**T*

= λ × f

=

= λ × f

In this way, we confirmed the simplified equation of waves

v = λ × f

obtained in the previous tutorial.

y(x,t) = y_{max} × 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.

Enjoy the "How to Obtain the Simplified Wave Equation from the General Equation of Waves" physics lesson? People who liked the "General Equation of Waves lesson found the following resources useful:

- Equation Feedback. Helps other - Leave a rating for this equation (see below)
- Waves Physics tutorial: General Equation of Waves. Read the General Equation of Waves physics tutorial and build your physics knowledge of Waves
- Waves Revision Notes: General Equation of Waves. Print the notes so you can revise the key points covered in the physics tutorial for General Equation of Waves
- Waves Practice Questions: General Equation of Waves. Test and improve your knowledge of General Equation of Waves with example questins and answers
- 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.
- Continuing learning waves - read our next physics tutorial: Energy and Power of Waves

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