A sinusoidal wave is propagating in negative x $$-direction$$ in a string stretched along $$x-axis$$. A particle of string at $$x=2$$ m is found at its mean position and it is moving in positive $$y-direction$$ at $$t=1sec$$. The amplitude of the wave, the wavelength and the angular frequency of the wave are $$0.1$$ meter, π$$/2$$ meter and $$2$$$$π$$$$rad/$$$$sec$$ respectively. The equation of the wave is

Question

A sinusoidal wave is propagating in negative x $$-direction$$ in a string stretched along $$x-axis$$. A particle of string at $$x=2$$ m is found at its mean position and it is moving in positive $$y-direction$$ at $$t=1sec$$. The amplitude of the wave, the wavelength and the angular frequency of the wave are $$0.1$$ meter, π$$/2$$ meter and $$2$$$$π$$$$rad/$$$$sec$$ respectively. The equation of the wave is

Infinity Learn · Accepted Answer

The equation of wave moving in negative x $$-direction$$,  assuming origin of position at $$x=2$$ and origin of time  (i$$.e. initial $$time) at $$t=1sec$$ . $$y=0.1sin(2$$$$π$$$$t+4x)$$ Shifting the origin of position to left by $$2$$ m , that is, to $$x=0$$ . Also shifting the origin of time backwards by $$1$$ $$sec$$ ,  that is to $$t=0sec$$ . $$y=0.1sin(2$$π(t$$−$$1)+4(x$$−$$2))

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