A string with mass per unit length 0.0065

Question

kg/m is used to suspend a 30 kg mass over a
pulley. A transverse wave with wavelength 40
cm and amplitude 2.5 mm moves along the
string. Determine the maximum speed of a
particle on the string.

Answer 1

y=A*sin(wt)
A=.0025m
f=wavespeed/wavelength

wavespeed=sqrt(Tension/(m/L))
= sqrt(30*9.8/(.0065)) m/s
wavelength=.4m
figure then frequency f.
w=2PI*f

y=Asin(wt)
y'=Aw cosWt which is particle velocity, so at cos wt=1
max partical velocity= .0025*2PI*f