Question

Plnti Plot: Figure 1: D(x) (m) vrs. r (m) Figure 2: D(t) (m) vrs. t (s) igure I: D(c) (m) vrs. m

The graph in Figure 1 shows the displacement versus position for the wave at t = 1:0 s. The graph in Figure 2 shows the displacement versus time for the wave at x = 1:0 m. Determine the displacement equation D(x,t) and the velocity of the wave. SHOW WORK

Answer 1

from the graphs we have

Amplitude A = 0.1m

wavelength $\lambda$ =4m

time period T = 2s

speed V = wavelength / time period = 4/2 = 2m/s

we have

$w = 2\pi /T = 3.14 s^{-1}$

$k= 2\pi /\lambda = 1.57 m^{-1}$

the equation of the wave is

D(x,t) = A sin (wt -kx)

D(x,t) = 0.1 sin(3.14t -1.57x)