Question

Y = 0.5 Sin ( 314 t - 1.5x) where t is measured in second, x and y are measured in metre respectively. Find wave length​

Answer 1

$\mathfrak{ \huge{ \red{ \underline{ \underline{Answer}}}}} \\ \\ \star \: \blue{ \sf{given}} \\ \\ \implies \sf \: y = 0.5 \sin(314t - 1.5x) \\ \\ \star \: \blue{ \sf{to \: find}} \\ \\ \implies \: \sf \: wavelength \: (\lambda) \\ \\ \star \: \blue{ \sf{calculation}} \\ \\ \implies \: \sf \: comparing \: with \: wave \: equation \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bold{ \red{ \sf{y = a \sin( \omega \: t - kx) }}}} \\ \\ \implies \: \sf \: k = 1.5 \\ \\ \implies \: \sf \: we \: know \: that \: \: \: \boxed{ \red{ \bold{k = \frac{2 \pi}{ \lambda} }}} \\ \\ \implies \sf \: \lambda = \frac{2 \pi}{1.5} = 4.186 \: m \\ \\ \\ \: \: \: \: \: \blue{ \huge{ \star}} \: \: \boxed{ \boxed{ \green{ \huge{ \bold{ \sf{ \lambda = 4.19 \: m}}}}}} \: \: \blue{ \huge{ \star}}$