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 $x^{\prime}=x-v t$ :

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