Question

A sinusoidal transverse wave of wavelength 19.0 cm travels along a string in the positive direction of an x axis. The displacement y of the string particle at x = 0 is given in the figure as a function of time t. The scale of the vertical axis is set by y_s = 4 cm. The wave equation is to be in the form of

y = y_m sin(kx - ωt + φ).

(a) At t = 0, is a plot of y versus x in the shape of a positive sine function or a negative sine function? What are (b) y_m, (c) k, (d) ω, (e) φ, (f) the sign in front of ω, and (g) the wave speed (speed of the wave along the string) and (h) What is the transverse velocity of the particle at x = 0 when t = 3.00 s?

Answer 1

ware length = d = 19cm = 0.19m. Ys = 4cm y=flt) = Yg Sin wt us=46m. w=24 25 T 14 ware it travelling along pusshire x-adig so tta y = fland) = ys Siml w14-X)] =Ys sin (wt-wox.) =Ys Sin /wt-test) y=-Ys Sim (ex-wt) =tys Som (a+kw-w+) y = Yg Sin (lex-w++2) 0 y=Ym Sim 1xen-woto) from ero & ERO ad Ym=Y8=4cm K=27 = 27 m2 = 33.07 m 7 wsze = 0.45 gadis o=* a) Atit=0, y = 4 Sin (x+x)=-4 finxx - negatiresine function a b) Ym = 4cm c> k=33•07 m dJ w = 0.45 rad Is e) o = i +)-ve al V-ware speed = “ = 0:45 - = 33.07 =13669) h) vy z velocity of particle=ay = wys of lwt - Kx) 30.45x4 coB (180x3) = 0.4 cmis 7 -1