d
(d) Standard wave equation which travel in negative \(x-\) direction is \(y = A\sin (\omega \,t + kx + {\varphi _0})\)

For the given wave \(\omega = 2\pi n = 15\pi ,\,\,k = \frac{{2\pi }}{\lambda } = 10\pi \)

Now \(v = \frac{{{\rm{Co - efficient \,of\, }}t}}{{{\rm{Co - efficient \,of \,}}x}}\) \( = \frac{\omega }{k} = \frac{{15\pi }}{{10\pi }} = 1.5\,m/sec\)

and \(\lambda = \frac{{2\pi }}{k} = \frac{{2\pi }}{{10\pi }} = 0.2\,m.\)