Answer to Question #88740 in Electricity and Magnetism for Shivam Nishad

Question

A transverse wave travelling in the positive
x-direction is represented as
y(x, t) = 5 sin (4.0 t - 0.02 x) cm.
Show that the ratio of maximum
acceleration of the particles of the medium . to
their maximum velocity is 4 : 1.

Answer 1

The maximum acceleration of the particles of the medium:

$$a=A\omega^2$$

The maximum velocity:

$$v=A\omega$$

Their ratio:

$$\frac{a}{v}=\omega=4$$