y (x, t) = 2asinkxcos ωt
This equation is similar to the equation:
$\mathrm{y}(\mathrm{x}, \mathrm{t})=0.06 \sin \left(\frac{2\mathrm{\pi }}{3}\mathrm{x}\right)\cos \left(120\mathrm{\pi t}\right)$
Hence, the given function represents a stationary wave.
A wave travelling along the positive x-direction is:
${\mathrm{y}}_1=\mathrm{a} \sin (\mathrm{\omega t}-\mathrm{kx})$

The wave travelling along the negative x-direction is:
${\mathrm{y}}_2=\mathrm{a} \sin (\mathrm{\omega t}+\mathrm{kx})$

The superposition of these two waves yields:

$\begin{array}{l}\mathrm{y}={\mathrm{y}}_1+{\mathrm{y}}_2=\mathrm{asin}(\mathrm{\omega t}-\mathrm{kx})-\mathrm{asin}(\mathrm{\omega t}+\mathrm{kx})\\ =\mathrm{asin}\left(\mathrm{\omega t}\right)\cos \left(\mathrm{kx}\right)-\mathrm{asin}\left(\mathrm{kx}\right)\cos \left(\mathrm{\omega t}\right)-\mathrm{asin}\left(\mathrm{wt}\right)\cos \left(\mathrm{kx}\right)-\mathrm{asin}\left(\mathrm{kx}\right)\cos \left(\mathrm{wt}\right)\\ =-2\mathrm{asin}\left(\mathrm{kx}\right)\cos \left(\mathrm{\omega t}\right)\\ =-2\mathrm{asin}\left(\frac{2\mathrm{\pi }}{\mathrm{\lambda }}\mathrm{x}\right)\cos \left(2\mathrm{\pi \nu t}\right) ...\left(\mathrm{i}\right)\end{array}$

The transverse displacement of the string is:

$\mathrm{y}(\mathrm{x}, \mathrm{t})=0.06\sin \left(\frac{2\mathrm{\pi }}{3}\mathrm{x}\right)\cos (120 \mathrm{\pi t}) ...\left(\mathrm{ii}\right)$

Comparing equations (i) and (ii),

$\mathrm{Wavelength}, \mathrm{\lambda }=3 \mathrm{m}$
$\mathrm{Frequency}, \mathrm{\nu }=60 \mathrm{Hz}$
$\mathrm{Wave} \mathrm{speed}, \mathrm{v}=\mathrm{\nu \lambda }=60\times 3=180 \mathrm{m}/\mathrm{s}$
$\mathrm{The} \mathrm{velocity} \mathrm{of} \mathrm{a} \mathrm{transverse} \mathrm{wave} \mathrm{travelling} \mathrm{in} \mathrm{a} \mathrm{string}:$
$\mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}} ...\left(\mathrm{i}\right)$
$\mathrm{Velocity} \mathrm{of} \mathrm{the} \mathrm{transverse} \mathrm{wave}, \mathrm{v} = 180 \mathrm{m}/\mathrm{s}$
$\mathrm{Mass} \mathrm{of} \mathrm{the} \mathrm{string}, \mathrm{m} = 3.0 \times {10}^2 \mathrm{kg}$
$\mathrm{Length} \mathrm{of} \mathrm{the} \mathrm{string}, \mathrm{l} = 1.5 \mathrm{m}$
$\mathrm{Mass} \mathrm{per} \mathrm{unit} \mathrm{length} \mathrm{of} \mathrm{the} \mathrm{string}, \mathrm{\mu }=\frac{\mathrm{m}}{\mathrm{l}}=\frac{3.0}{1.5}\times {10}^{-2}=2\times {10}^{-2} \mathrm{kg} {\mathrm{m}}^{-1}$
$\mathrm{Tension} \mathrm{in} \mathrm{the} \mathrm{the} \mathrm{string},$
$\mathrm{T} = {\mathrm{v}}^2\mathrm{\mu }$
$= {\left(180\right)}^2 \times 2 \times {10}^{-2}$
$= 648 \mathrm{N}$