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 0.345 m. The waves travel in the -x-direction, and at t = 0 the x = 0 end of the string has its maximum upward displacement. (a) Find the following properties of these waves. frequency f , period T , wave number k (b) Write a wave function describing the wave. (Use the following as necessary: t and x.) y(x, t) = (c) Find the transverse displacement of a particle at x = 0.360 m at time t = 0.150 s. cm (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?

NOTE: PART A-C ANSWERS BELOW ARE CORRECT. NEED HELP ON PART D. PLEASE SHOW STEP BY STEP AND EXPLAIN. ANSWERS OF SIMILAR PROBLEMS ON CHEGG ARE INCORRECT.

Explanation / Answer

d) The particle at 0.360 m will be having next maximum upward displacement when value of angle inside cosine is even multiple of pi.
at t = 0.150 s, the value of angle = 145.69*0.15+18.21*0.36 = 28.4091 = 8 pi - 3.276.
So the needed angle is 3.276 radians so the elapsed time = 3.276/145.69 = 0.022 sec.

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