The displacement of a wave is given by $\mathrm{Y}=5 imes 10^{-3} \operatorname{Sin}(100 \mathrm{t

Question

The displacement of a wave is given by $\mathrm{Y}=5 	imes 10^{-3} \operatorname{Sin}(100 \mathrm{t}-50 \mathrm{x})$ where ' t ' is expressed in seconds and ' $x$ ' in meters. The velocity of wave is\

Professor PC Thomas Classes · Answer

$E=5 	imes 10^{-2} \sin (100 t-50 x)$ (1) Given Eqn\ $Y=A \sin \frac{2 \pi}{\lambda}(v t-x)(2)$\ Standard Eqn.\ Comparing (1) and (2) (1)$A=5 	imes 10^{-2}$ (amplitude) (2)Compare coeff: of metre. Thus to get $\lambda$, compare coeff: of $x$ only\ 3) Compare coeff: $t$\ $2 \pi \frac{\mathrm{~V}}{\mathrm{~K}}=100$\ $\frac{\mathrm{v}}{\lambda}=\frac{100}{2 \pi}$\ $\frac{\mathrm{v}}{\lambda}$ is frequency. $	herefore$ Frequency $=\frac{100}{2 \pi}$\ Thus to get frequency compare the coeff: of only 4) To get velocity First compare coeff: of x . Get wavelength $\lambda$. Then compare coeff: of . Get frequency $\gamma$. The velocity $
u=\gamma \lambda \lambda$\ Here $\lambda=\frac{2 \pi}{50}$\ $\gamma=\frac{100}{2 \pi}$ $$ v=\gamma \lambda $$