Physics - Wave on String Question with Solution | TestHub

The given wave equation is

$y = A\sin (\omega t – kx)$

$\text{Wave velociy,}\mathit{\text{v}}=\frac{\omega }{k}\dots \left(\text{i}\right)$

$\text{Particle velocity,}{\mathit{\text{v}}}_p=\frac{dy}{dt}=A\omega \text{cos}\left(\omega t-kx\right)$

Maximum particle velocity,${\left(v_{\text{p}}\right)}_{\text{max}}=\mathit{\text{A}}\omega$...(ii)

According to the given question

$v={\left(v_{\text{p}}\right)}_{\text{max}}$

$\frac{\omega }{k}=A\omega \left(\text{Using (i) and (ii)}\right)$

$\frac{1}{k}=A$

$\text{or}\frac{\lambda }{2\pi }=A\left(\because k=\frac{2\pi }{\lambda }\right)$

$\lambda = 2\pi A$