Dimensional analysis equation help

[mooneh]

y = (2m) cos (kx), where k = 2 m^-1

it says that the equation is dimensionally correct but i don't understand why...

 

[G01]

I'll assume y is a distance, such as the position of a point on a wave. Consider this:

What are the units of all the terms in the equation? i.e. the units of the 2 outside the cosine, and the units of what is in the cosine argument.

Using dimensional analysis, what are the units of y?

 

[ogb p]

Dimensional analysis is a mathematical tool used to check the consistency of equations by analyzing the units of measurement involved. In this equation, we have two variables, y and x, which have units of length. The variable m represents a distance, and k represents a wavenumber, which has units of inverse length (m^-1).

When we substitute these units into the equation, we get:

y = (2m) cos (kx)
= (2m) cos (2 m^-1 * x)

We can see that the units of m and m^-1 cancel each other out, leaving us with just the unit of length for y. This means that the equation is dimensionally consistent, as the units on both sides of the equation match.

In addition, the trigonometric function cos does not have any units, so it does not affect the dimensional analysis of the equation. Therefore, the equation is dimensionally correct.