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  4. A transverse wave is represented by y =2 sin (ω t - kx ) cm. The value of wavelength (in cm ) for which the wave velocity becomes equal to the maximum particle velocity, will be ;

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Q. A transverse wave is represented by $y =2 \sin (\omega t - kx ) cm$. The value of wavelength (in $cm$ ) for which the wave velocity becomes equal to the maximum particle velocity, will be ;

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Solution:

$ y=2 \sin (\omega t-k x) $
Maximum particle velocity $=\text { A } \omega $
Wave velocity $=\frac{\omega}{ k } $
$ \frac{\omega}{ k }= A \omega $
$ k =\frac{1}{ A }=\frac{2 \pi}{\lambda} $
$ \lambda=2 \pi A $
$ =4\, \pi\, cm$