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 ..... $cm$ ?
JEE MAIN 2014, Medium
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Given, amplitude $a$ $=10 \mathrm{cm}$
wave velocity $=2 \times$ maximum particle velocity
i.e, $\frac{{\omega \lambda }}{{2\pi }} = 2\frac{{{\rm{a}}\omega }}{\pi }$
or, $\quad \lambda=4 \mathrm{a}=4 \times 10=40 \mathrm{cm}$
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