Question

A transverse 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.

Answer 1

A) 0.33 m/s

Step-by-step 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