Travelling Waves - Practice Questions & MCQ

The function f(t) represnents the displacements y of the particle at x=0 as a function of time y(x,t)=f(t). The disturbance travels on the strings towards right with a constant speed 'v'. Thus, the displacement produced at the left end at time 't', reaches the point 'x' at time 't+x/v'.

There's a good reason for the factor of 2π. Looking at this expression, we can see that, when x' increases by λ, the argument of the sine function increases by 2π, so the sine function goes through one complete cycle. Let's now write the equation in terms of the stationary coordinate x, where x'  =  x − vt :