Atransverse wave is traveling on a string stretched along the horizontal x-axis. the equation for the
vertical displacement y of the string is given by y = 0.0020 cos[? (15x - 52t)], where all quantities are in
si units. the maximum speed of a particle of the string is closest to
a) 0.33 m/s.
b) 0.43 m/s.
c) 0.53 m/s.
d) 0.64 m/s.
e) 0.74 m/s.

A) 0.33 m/s

Explanation:

The standard form of a transverse wave is given by  

y = a  cos ( ω t − kx ) ,   k =  2 π  / λ

Amplitude,   a =  0.002  m

Wavenumber (k)=47.12 and wavelength  ( λ )  =  0.133 m

Time period(T)=0.0385 s and angular frequency  ( ω )  =  52 π  rad/s

Maximum speed of the string is given by  aw

Therefore ; max. speed = 0.002 x 52 π = 0.327 m/s

option number c is the right answer.