Amplitude in time and in space

Problem

A graph shows $y(x)$ at a fixed time and a second one $y(t)$ at a fixed position. What information can be read from each? How is the speed obtained?

Solution

Graph $y(x)$ (snapshot at fixed $t$). This is a snapshot of the wave along space: from the axis one reads the wavelength $\lambda$ (distance between two consecutive crests) and the amplitude $A$. It gives no information about the period.

Graph $y(t)$ (oscillation at fixed $x$). This follows the motion of a single point over time: one reads the period $T$ (time between two consecutive crests), from which the frequency

$f = \frac{1}{T}$

and again the amplitude $A$.

Propagation speed. Combining the two pieces of information:

$v = \lambda\,f = \frac{\lambda}{T}$

$\ev{\text{From } y(x)\!: \lambda;\ \text{from } y(t)\!: T \text{ and } f=1/T;\ \text{then } v=\lambda f.}$

Neither graph alone gives the speed: both are needed (one spatial scale and one temporal scale).

Linked atoms

Topics: Onde Concepts: Onda armonica Skills: Lettura dei grafici