Question

Is `y=(2m)*cos(k*x)` dimensionally correct, where `k = 2m^-1`?

This question is from Chapter 1.4, "Dimensional Analysis" of Serway's Physics (4th Edition). It comes from homework problem 13.b

Answer 1

No, it is not dimensionally correct.

Explanation:

Let `m = L` for length
Let `k = 2/L` for the given `m^-1`
Let `x` remain an unknown variable. Plugging these into the original equation gives us:

`y=(2L)*cos(2/L*x)`

Letting the dimensions absorb the constants, we have

`y=(L)*cos(x/L)`

This puts units inside of a cosine function. However, a cosine function will simply output a non-dimensional value between `+-1`, not a new dimensional value. Therefore, this equation is not dimensionally correct.