A sinusoidal transverse wave of amplitude ym = 6.4 cm and wavelength = 5.2 cm travels on a stretched cord. Find the ratio of the maximum particle speed (the speed with which a single particle in the cord moves transverse to the wave) to the wave speed.

Answer 1

I assume you have had calculus

y=Asinwt
where A is 6.4cm
f=wavespeed/lambda

w=2PIf=2PIwavspeed/lambda

y=Asinwt
y'=particle speed=Awcoswt=A2PI (wavespeed)/lambda

the maximum occurs at coswt=1
solve for particle speed/wavespeed.