A transverse wave propagating along x-axis is represented by:

$straight y left parenthesis straight x comma space straight t right parenthesis space equals space 8.0 space sin space open parentheses 0.5 πx minus 4 πt minus straight pi over 4 close parentheses$
where x is in metres and t is in seconds. The speed of the wave is

$4 straight pi$ m/s
$0.5 straight pi space straight m divided by straight s$
$straight pi over 4 straight m divided by straight s$

8 m/s

Solution

8 m/s

The standard transverse wave propagating along x-axis can be written as
$straight y equals straight a space sin space left parenthesis kx space minus space ωt plus space straight ϕ right parenthesis$
The given equation is
$straight y left parenthesis straight x comma space straight t right parenthesis space equals space 8.0 space sin space open parentheses 0.5 space straight pi space straight x space minus space 4 πt minus straight pi over 4 close parentheses space space space space space space space space... left parenthesis 1 right parenthesis$
The standard wave equation can be written as,
$straight y space equals space straight a space sin space left parenthesis kx minus ωt plus straight ϕ right parenthesis$ ...(2)
where $straight alpha$ is amplitude, k the propagation constant and $straight omega$ the angular frequency,
comparing the Eqs. (i) and (ii), we have
$straight k space equals space 0.5 space straight pi comma space space space straight omega space equals space 4 straight pi$
$therefore$ Speed of transverse wave
$straight v equals straight omega over straight k equals fraction numerator 4 straight pi over denominator 0.5 straight pi end fraction space equals space 8 space straight m divided by straight s$