Question

Calculate a wave velocity when a force of 500 acts on a system with mass per unit length 0.25kg/m

Answer 1

Assuming the force acting as tension in a string;

Force, F = 500N
linear mass density, μ = 0.25 kg/m
v = ?

$v= \sqrt{ \frac{F}{\mu } } =\sqrt{ \frac{500}{0.25 } }\ m/s= \sqrt{2000}\ m/s\\ \\ v=20 \sqrt{5}\ m/s \\ \\ v=44.72\ m/s$

Answer 2

  Force F = 500 Newtons / unit length

   mass / unit length of the system = 0.25 kg / meter = mass/length

   acceleration a = F / m =  500 / 0.25
                = 2,000  m/sec² 
         assuming that the force is acting uniformly along the length of the system.
 
   velocity = u + a t = at  if initial velocity u = 0,  as the system starts from rest.

     v = 2,000 t,                where t = time.