# NEET Physics Waves Questions Solved

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A transverse wave is represented by the equation $y={y}_{0}\mathrm{sin}\frac{2\pi }{\lambda }\left(vt-x\right)$

For what value of λ, the maximum particle velocity equal to two times the wave velocity

(1) $\lambda =2\pi {y}_{0}$

(2) $\lambda =\pi {y}_{0}/3$

(3) $\lambda =\pi {y}_{0}/2$

(4) $\lambda =\pi {y}_{0}$

(4) On comparing the given equation with standard equation $y=a\mathrm{sin}\frac{2\pi }{\lambda }\left(vt-x\right)$. It is clear that wave speed ${\left(v\right)}_{wave}=v$ and maximum particle velocity ${\left({v}_{\mathrm{max}}\right)}_{particle}=a\omega ={y}_{0}×$ co-efficient of t $={y}_{0}×\frac{2\pi v}{\lambda }$

$\because \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\left({v}_{\mathrm{max}}\right)}_{particle}=2{\left(\omega \right)}_{wave}$$\frac{a×2\pi v}{\lambda }=2v$$\lambda =\pi {y}_{0}$

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