Question

A transverse wave passes through a string with the equation y= (10 cm) sin π (0.02x - 2.00t) where x is in metre and t in second. The maximum velocity of the particles in wave motion is (in cm/s)​ a) 63 b) 78 c) 100 d) 121

Answer 1

Dear Student,

$$\begin{gathered} y=\left(10cm\right)\sin \mathrm{\pi }\left(0.02\mathrm{x}-2.00\mathrm{t}\right) \\ \mathrm{or},\mathrm{y}=\left(10\mathrm{cm}\right)\sin \left(0.02\mathrm{\pi x}-2.00\mathrm{\pi t}\right)................\left(1\right) \\ \mathrm{comparing}\mathrm{the}\mathrm{equation}\left(1\right)\mathrm{with} \\ \mathrm{y}=\mathrm{A}\sin \left(\mathrm{\omega t}-\mathrm{kx}\right) \\ \mathrm{A}=10\mathrm{cm} \\ \mathrm{\omega }=2\mathrm{\pi } \\ \mathrm{maximum}\mathrm{velocity},\mathrm{v}=\mathrm{A\omega } \\ \mathrm{v}=10\times 2\times 3.14 \\ \mathrm{v}=62.8\approx 63\mathrm{cm}/\mathrm{s} \end{gathered}$$