A transverse wave is represented by $y=A \sin (\omega t-k x)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

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Aicharya · Accepted Answer

Wave velocity $\mathrm{v}=\frac{\lambda}{\mathrm{T}}=\frac{\omega \lambda}{2 \pi}$ Maximum particle velocity $\left(v_{\max }ight)_p=A \omega$ Given, $\begin{aligned} & \mathrm{v}=\left(\mathrm{v}_{\max }ight)_p \ & \frac{\omega \lambda}{2 \pi}=A \omega \ & \Rightarrow \quad \lambda=2 \pi \mathrm{A} \ & \end{aligned}$

A transverse wave is represented by $y=A \sin (\omega t-k x)$. For what value of the wavelength is the wave…

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