Physics - Wave on String Question with Solution | TestHub

General equation of a simple harmonic progressive wave, $y=A\sin 2\pi \left[\frac{t}{T}-\frac{x}{\lambda }\right]$ Given: $y=a\sin 2\pi (bt-cx)$ $\Rightarrow \mathrm{A}=\mathrm{a},\frac{1}{\mathrm{T}}=\mathrm{b}\text{ and }\frac{1}{\lambda }=\mathrm{cx}$ Also, ${\left(v_p\right)}_{\max }=a\omega =a(2\pi n)=\frac{a2\pi }{T}$ $=\frac{\mathrm{A}2\pi }{\mathrm{T}}=\mathrm{a}2\pi \mathrm{b}$ From $\mathrm{v}=\frac{\lambda }{\mathrm{T}}=\frac{1/\mathrm{c}}{1/\mathrm{b}}=\frac{\mathrm{b}}{\mathrm{c}}$ Given: ${\left({\mathrm{v}}_{\mathrm{p}}\right)}_{\max }=\frac{1}{2}\mathrm{v}$ $\begin{array}{rl}\Rightarrow & 2\pi \mathrm{ab}=\frac{1}{2}\times \frac{\mathrm{b}}{\mathrm{c}}\\ \therefore \mathrm{c}& =\frac{1}{4\pi \mathrm{a}}\end{array}$