Physics - Wave on String Question with Solution | TestHub

$y\left(x,t\right)=8·0\text{sin}\left(0·5\pi x-4\pi t-\frac{\pi }{4}\right)$

Compare with a standard wave equation,

$y=a\text{sin}\left(\frac{2\pi x}{\lambda }-\frac{2\pi t}{T}+\varphi \right)$

$\text{we get }\frac{2\pi }{\lambda }=0·5\pi \text{or,}\lambda =\frac{2\pi }{0·5\pi }=4\text{m}$

$\frac{2\pi }{T}=4\pi \text{or,}T=\frac{2\pi }{4\pi }=\frac{1}{2}s$

$\upsilon =1/\mathit{\text{T}}=\text{2 Hz}$

Wave velocity,$\nu =\lambda \upsilon =4\times 2=8 \mathrm{m} {\mathrm{s}}^{-1}$