A wave in a string has an amplitude of 2 ~cm . The wave travels in...

Key Idea Find the parameters and put in the general wave equation. Here, \begin{aligned} A & =2 \mathrm{~cm} \\ \text { direction } & =+ \text { ve direction } \\ \mathrm{v} & =128 \mathrm{~ms}^{-1} \end{aligned} and $$5 \lambda=4$$ Now, $$\mathrm{k}=\frac{2 \pi}{\lambda}=\frac{2 \pi \times 5}{4}=7.85$$ and $$\mathrm{v}=\frac{\omega}{\mathrm{k}}=128 \mathrm{~ms}^{-1}$$\begin{aligned} \Rightarrow \quad \omega & =\mathrm{v} \times \mathrm{k}=128 \times 7.85 \\ & =1005 \end{aligned}\begin{array}{lll} \text { As, } & y & =\mathrm{A} \sin (\mathrm{kx}-\omega \mathrm{t}) \\ \therefore & & \mathrm{y}=2 \sin (7.85 \mathrm{x}-1005 \mathrm{t}) \\ & & =(0.02) \mathrm{m} \sin (7.85 \mathrm{x}-1005 \mathrm{t}) \end{array}