Travelling Waves MCQ - Practice Questions with Answers

The function f(t) represents 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 rthe ight with a constant speed of 'v'. Thus, the displacement produced at the left end at time 't', reaches the point 'x' at time 't+x/v'.

$$y=\sin \left(\frac{2\pi x^{\prime }}{T}\right)$$

There's a good reason for the factor of $2\pi$. Looking at this expression, we can see that, when $x$ ' increases by $\lambda$, the argument of the sine function increases by $2\pi$, so the sine function goes through one complete cycle. Let's now write the equation in terms of the stationary coordinate $x$, where $x^{\prime }=x-vt$ :

$$y=\sin \left(\frac{2\pi (x-vt)}{\lambda }\right)$$