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  4. A transverse wave is represented by: y = (10/π) sin ((2π/T)t-(2π/λ)x) For what value of the wavelength the wave velocity is twice the maximum particle velocity ?

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Q. A transverse wave is represented by :
$y = \frac{10}{\pi} \sin \left(\frac{2\pi}{T}t-\frac{2\pi}{\lambda}x\right)$
For what value of the wavelength the wave velocity is twice the maximum particle velocity ?

JEE MainJEE Main 2014Waves

Solution:

$V=2\left(V_{p}\right)_{max}$
$\because V=f \lambda$
$f \lambda =2\omega A$
$\lambda =4\pi A$
$=4\pi\times\frac{10}{\pi}$
$=40\,cm$