Question
The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given by $\text{f(t)}=\text{a}\sin\Big(\frac{\text{t}}{\text{T}}\Big).$ The wave speed is v. Write the wave equation.
✓
Answer
At x = 0, $\text{f(t)}=\text{a}\sin\Big(\frac{\text{t}}{\text{T}}\Big).$ Wave speed = v$\Rightarrow\lambda$ = wavelength = vT (T = Time period)
So, general equation of wave$\text{Y}=\text{A}\sin\bigg[\Big(\frac{\text{t}}{\text{T}}\Big)-\Big(\frac{\text{x}}{\text{vT}}\Big)\bigg]$ $\Bigg[$ because $\text{y}=\text{f}\bigg(\Big(\frac{\text{t}}{\text{T}}\Big)-\Big(\frac{\text{x}}{\lambda}\Big)\bigg)\Bigg]$
So, general equation of wave$\text{Y}=\text{A}\sin\bigg[\Big(\frac{\text{t}}{\text{T}}\Big)-\Big(\frac{\text{x}}{\text{vT}}\Big)\bigg]$ $\Bigg[$ because $\text{y}=\text{f}\bigg(\Big(\frac{\text{t}}{\text{T}}\Big)-\Big(\frac{\text{x}}{\lambda}\Big)\bigg)\Bigg]$
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$
r =3.0 t \hat{ i }+2.0 t^2 \hat{ j }+5.0 \hat{ k }
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