Question

The displacement wave is given by y(x,t)=0.25*10^-3 sin(500t-0.25x) deduce amplitude,period,angular frequency,wavelength and amplitude of particle velocity where x is in cm ,t is in seconds,displacement y is in m

Answer 1

$$\begin{gathered} y=0.25*{10}^{-3}\sin \left(500t-0.25x\right) \\ y=A\sin \left(\omega t-kx\right) \\ amplitudeA=0.25*{10}^{-3}m \\ T=\frac{2\pi }{\omega }=\frac{2\pi }{500}sec. \\ f=\frac{500}{2\mathrm{\pi }}=\frac{250}{\mathrm{\pi }}Hz. \\ k=\frac{2\mathrm{\pi }}{\lambda } \\ \lambda =\frac{2\mathrm{\pi }}{0.25}=8\mathrm{\pi }\mathrm{cm}. \\ {\mathrm{V}}_{\max }=\mathrm{A\omega }=0.25*{10}^{-3}*500=0.125\mathrm{m}/\mathrm{s} \\ \mathrm{Regards} \end{gathered}$$