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(B) The general equation for a travelling wave is $y = a \sin(\omega t - kx + \phi_0)$.At $t=0$ and $x=0$,$y=0$,which implies $\phi_0 = 0$.Thus,the wa

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$-0.02$

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(B) The general equation for a travelling wave is $y = a \sin(\omega t - kx + \phi_0)$.At $t=0$ and $x=0$,$y=0$,which implies $\phi_0 = 0$.Thus,the wave equation is $y = a \sin(\omega t - kx)$.Given frequency $f = 500 \,Hz$ and speed $v = 100 \,m/s$,we calculate:$\omega = 2\pi f = 2\pi 	imes 500 = 1000\pi \,rad/s$.$k = \frac{\omega}{v} = \frac{1000\pi}{100} = 10\pi \,m^{-1}$.So,$y = a \sin(1000\pi t - 10\pi x)$.At $t=0$ and $x=0.25 \,m$,$y = 0.02 \,m$:$0.02 = a \sin(0 - 10\pi 	imes 0.25) = a \sin(-2.5\pi) = a \sin(-2\pi - 0.5\pi) = -a \sin(0.5\pi) = -a(1)$.Thus,$a = -0.02 \,m$.The wave equation is $y = -0.02 \sin(1000\pi t - 10\pi x)$.At $t = 5 	imes 10^{-4} \,s$ and $x = 0.2 \,m$:$y = -0.02 \sin(1000\pi 	imes 5 	imes 10^{-4} - 10\pi 	imes 0.2) = -0.02 \sin(0.5\pi - 2\pi) = -0.02 \sin(-1.5\pi) = -0.02 \sin(0.5\pi) = -0.02 	imes 1 = -0.02 \,m$.

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