Problem — Reading lambda and T from a wave graph

Problem

The figure shows a snapshot of a transverse wave along a string at instant $t = 0$ (top panel) and the oscillation in time of the point $x = 0$ (bottom panel). Read $\lambda$ and $T$ from the graph, then calculate the propagation speed.

Solution

Reading the top panel (space). The wave completes a full cycle every $4$ units of the $x$ axis: the distance between two consecutive maxima is

$\lambda = 4{,}0\;\mathrm{m}$

Reading the bottom panel (time). The point $x=0$ repeats its oscillation every $0{,}4$ s:

$T = 0{,}40\;\mathrm{s}$

Propagation speed.

$v = \frac{\lambda}{T} = \frac{4{,}0}{0{,}40} = \ev{10\;\mathrm{m/s}}$

Linked atoms

Argomenti: Waves Concetti: Period and frequency Competenze: Graph reading