Your answer is partially correct. Try again. For a certain transverse standing w

Question

Your answer is partially correct. Try again. For a certain transverse standing wave on a long string, an antinode is atx= 0 and an adjacent node is at x= 0.30 m. The displacement y() of the string particle atx:0 shown in the figure, where the scale of the y axis is set by ys-42 cm When t = 0.60 s, what is the displacement of the string particle at a x=040 m and b) x = 0.50 m ? What is the transverse velocity of the string particle at x 40 m at(c)060 s and d 1.2 s? 3s 152 Units l m (a) Number TT0.06919 (b) Number to 0399 Uritst Units T m/s (c) Number T-0.07062 Units Tl m/s (d) Number TT-0.1849

Explanation / Answer

T = 2 s

w = 2pi / T = pi or 3.14 rad/s

y = - A sin(wt)

y = - 4.2 cm sin(pi t)

k = 2 pi / lambda = 2 pi / (4 x 0.30) = 1.67 pi

y = - 4.2 cm sin( 1.67 pi x - pi t )

(A) t = 0.60s and x = 0.40 m

y = - 0.89 cm

(b) t = 0.60 x = 0.50

y = -2.83 cm

(c) vy = dy/dt = -13.2 cm/s cos( 1.67 pi x - pi t )

x =0.40 , t = 0.60

vy = - 12.9 cm/s

(d) vy = 1.32 cm/s

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