The equation of simple harmonic progressive wave is given by $y=a \sin 2 \pi(b t-c x)$. The maximum particle velocity will be half the wave velocity, if $\mathrm{c}=$

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Aicharya · Accepted Answer

General equation of a simple harmonic progressive wave, $y=A \sin 2 \pi\left[\frac{t}{T}-\frac{x}{\lambda}ight]$ Given: $y=a \sin 2 \pi(b t-c x)$ $\Rightarrow \mathrm{A}=\mathrm{a}, \frac{1}{\mathrm{~T}}=\mathrm{b} 	ext { and } \frac{1}{\lambda}=\mathrm{cx}$ Also, $\left(v_pight)_{\max }=a \omega=a(2 \pi n)=\frac{a 2 \pi}{T}$ $=\frac{\mathrm{A} 2 \pi}{\mathrm{T}}=\mathrm{a} 2 \pi \mathrm{b}$ From $\mathrm{v}=\frac{\lambda}{\mathrm{T}}=\frac{1 / \mathrm{c}}{1 / \mathrm{b}}=\frac{\mathrm{b}}{\mathrm{c}}$ Given: $\left(\mathrm{v}_{\mathrm{p}}ight)_{\max }=\frac{1}{2} \mathrm{v}$ $\begin{aligned} \Rightarrow & 2 \pi \mathrm{ab}=\frac{1}{2} 	imes \frac{\mathrm{b}}{\mathrm{c}} \ 	herefore \quad \mathrm{c} & =\frac{1}{4 \pi \mathrm{a}} \end{aligned}$ .

The equation of simple harmonic progressive wave is given by $y=a \sin 2 \pi(b t-c x)$. The maximum particle…

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