Equation for a travelling wave is y=a‌sin(ωt−kx+φ0) As at t=0 at x=0 and y=0, φ0=0 ⇒‌‌φ0=0 So, equation of wave over string is Here, y‌‌=a‌sin(ωt−kx) ω‌‌=2πf=2π×500 ‌‌=1000π(‌
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) Here, Angular wave number, k=‌ω∕v=‌1000π∕100=10π(m−1) So, wave equation is y=a‌sin(1000π⋅t−10π⋅x) Given at t=0 at x=0.25m and y=0.02m. So, ‌‌0.02=a‌sin(−10π×0.25) =−a‌sin(‌5∕2π) [∴sin(−θ)=−sin‌θ] ⇒‌‌0.02=−a‌sin(2π+‌π∕2) ⇒‌‌0.02=−a‌sin(‌π∕2) or a=−0.02 Here note that a is amplitude and its positive and negative values are same. When we are getting a negative value this means particle is displaced below mean position. So, we have y=−0.02‌sin(1000πt−10πx) Now, at t=5×10−4s and x=0.2m, value of displacement of particle is y‌‌=−0.02‌sin(1000π×5×10−4 ‌‌=−0.02‌sin(‌