The equation of sound wave is given by $y=2\sin (314t-4x+\pi /2)$ the wave length of the wave is:

A progressive wave is one that travels continuously in a medium without changing in amplitude or direction and is given by the equation

$\Rightarrow Y=ASin(Kx-\omega t)$
Here$\mathrm{A}=$ Amplitude $\mathrm{K}=$ Wave vector, $\mathbf{t}=$time and $\mathrm{x}=$distance
The wave vector is the quantity used to express the amount and direction of motion, which is given by
$\Rightarrow K=\frac{2\pi }{\lambda }$

The wave vector is the quantity used to express the amount and direction of motion, which is given by

$\Rightarrow K=\frac{2\pi }{\lambda }$
Here $\lambda =$Wavelength
Given $y=2\sin (314t-4x+\pi /2)$
The equation of progressive wave is given by
$\Rightarrow Y=A\sin (KX-\omega t)$

Comparing the given equation to the above equation
$\Rightarrow K=4$
The wave vector is given by
$\Rightarrow \frac{2\pi }{\lambda }=4$
$\lambda =\frac{2\pi }{4}=\frac{\pi }{2}=1.57 \mathrm{m}$
Hence, option 4 is the answer