Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0550 m, and w

Question

Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0550 m, and wavelength 0.330 m. The waves travel in the -x-direction, and at t = 0 the x = 0 end of the string has its maximum upward displacement.

(c) Find the transverse displacement of a particle at x = 0.360 m at time t = 0.150 s.
(d) How much time must elapse from the instant in part (c) until the particle at x = 0.360 m next has maximum upward displacement?
Please help me to solve c question in details. I try to pugged in the equation I got which is y(x,t)=0.0550cos(19x+152.24t), but it have the negative number (-0.9257cm)

Explanation / Answer

k = 2 pi / lambda = 2 pi / 0.330 = 19.03 m-1

f = v / lambda = 8.00 / 0.330 = 24.24 hz

w = 2 pi f = 152.3 rad/s

y ( x , t ) = 0.0550 * cos( 19.03 x + 152.3 t)

plug y( 0.360 , 0.150 ) = 0.0550 * cos( 6.85 + 22.845)

= 0.0550 * 0.8687 = 0.048 m

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