Fourier tells us that we can write a "pulse" by summing up sinusoidal functions:

$f(x) = \int_{-\infty}^{\infty} a(k)e^{ikx}dk$

If we were to compute $f(x) = \int_{-\infty}^{\infty} a(k)e^{ik(x-vt)}dk$ where $v$ is a known constant, what would we get?

1. $f(x)$
2. $f(vt)$
3. $f(x-vt)$
4. Something complicated!
5. ???

Fourier tells us that we can write a "pulse" by summing up sinusoidal functions:

$f(x) = \int_{-\infty}^{\infty} a(k)e^{ikx}dk$

If we were to compute $f(x) = \int_{-\infty}^{\infty} a(k)e^{ik(x-v(k)t)}dk$ where $v(k)$ is function, what would we get?

1. $f(x)$
2. $f(vt)$
3. $f(x-vt)$
4. Something more complicated!
5. ???