Solving Wave Propagation & Particle Speed Problems

[kali0712]

Hi! If anyone could help me with this problem I'd be deeply appreciative:

Speed of Propagation vs. Particle Speed. The equation y(x,t)=A cos2(pi)f (x/v - t) may be written as y(x,t)= A cos[(2(pi)/lamda)(x-vt)]

a) Use the last expression for y(x,t) to find an expression for the transverse velocity v_y of a particle in the string of which the wave travels.

b) Find the maximum speed of a particle of the string?


I really have no idea how I'm even meant to approach this problem... Anyone know how to figure it out?

Thanks!

 

[quasar987]

a) y(x,t) is the height at which the particle of the string at position x and time t is. If you only want to look at one particle of the string, fix x to say $x_0$ and look only at how the height y(t) varies with time. This, then is the equation of motion of that particle, since it gives its positon as a function of time. How can you find the velocity if you know the equation of motion?

b) One you have found an expression for the velocity in a), finding the maximum value is a basic calculus problem.

 

[ryane26]

Io being what? an initial value of 0?