Comparing Lag Between f(x,t) and g(x,t): Homework Equations and Solutions"

[Pushoam]

Homework Statement

We have $f(x,t) = cos(kx - \omega t) \\ g(x,t) = cos(kx - \omega t + \epsilon )$

How to find out whether f lags behind g or vice -versa?

Homework Equations

The Attempt at a Solution

I took, x =0,

g (t') = f(t)

$- \omega t' + \epsilon = - \omega t$
$t' = t + \frac { \epsilon }{\omega}$

If $\epsilon$ > 0, then t'> t, thus g lags behind f.

And if $\epsilon < 0$ , then t'<t , thus f lags behind g.

Is this correct?

Or is there any other way to find quickly just by seeing the functions?

 

[mfb]

Is this correct?

Right, assuming ω>0.

Or is there any other way to find quickly just by seeing the functions?

To get the same argument as before after introducing a positive $\epsilon$ in the second function, you need a larger t: You have to wait longer.