The mathematical forms for three sinusoidal traveling waves are given by

wave $1$: $y(x,t)=(2cm)sin[(3m^{-1})x-(6s^{-1})t]$

wave $2$: $y(x,t)=(3cm)sin[(4m^{-1})x-(12s^{-1})t]$

wave $3$:$y(x,t)=(4cm)sin[(5m^{-1})x-(11s^{-1})t]$

where $x$ is in meters and $t$ is in seconds. Of these waves,

Wave $2$ has the greatest wave speed, and wave $1$ has the greatest maximum transverse string speed.

Wave $3$ has the greatest wave speed and the greatest maximum transverse string speed.

Wave $1$ has the greatest wave speed and the greatest maximum transverse string speed.

Wave $2$ has the greatest wave speed, and wave $3$ has the greatest maximum transverse string speed.

Wave $3$ has the greatest wave speed, and wave $2$ has the greatest maximum transverse string speed.