1 $y(x, t)=2 \sin (2 x-2 t)$
2 $y(x, t)=3 \sin (2 x-3 t)$
3 $y(x, t)=2 \sin (3 x-2 t)$
4 $\mathrm{y}(\mathrm{x}, \mathrm{t})=3 \sin (5 \mathrm{x}-2 \mathrm{t})$
Explanation:
B (a) $y(x, t)=2 \sin (2 x-2 t) \quad \ldots . .(i)$
Comparing equation (i) with standard equation
$\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}-\omega \mathrm{t})$
$\mathrm{A}=2, \mathrm{k}=2, \omega=2 \mathrm{rad} / \mathrm{sec}$
We know that,
$\text { Wave speed }(v)=\frac{\omega}{k}=\frac{2}{2}=1 \mathrm{~m} / \mathrm{sec}$
(b) $y(x, t)=3 \sin (2 x-3 t)$
Comparing equation (ii) with standard equation
$\mathrm{A}=3, \mathrm{k}=2, \omega=3 \mathrm{rad} / \mathrm{sec}$ Wave speed $(\mathrm{v})=\frac{\omega}{\mathrm{k}}=\frac{3}{2}=1.5 \mathrm{~m} / \mathrm{sec}$
(c) $y(x, t)=2 \sin (3 x-2 t)$
Comparing equation (iii) with standard equation
$\mathrm{A}=2, \mathrm{k}=3, \omega=2 \mathrm{rad} / \mathrm{sec}$
Wave speed $(\mathrm{v})=\frac{\omega}{\mathrm{k}}=\frac{2}{3} \mathrm{~m} / \mathrm{sec}$
(d) $y(x, t)=3 \sin (5 x-2 t)$
Comparing equation (iv) with standard equation
$\mathrm{A}=3, \mathrm{k}=5, \omega=2 \mathrm{rad} / \mathrm{sec}$
Wave speed $(\mathrm{v})=\frac{\omega}{\mathrm{k}}=\frac{2}{5} \mathrm{rad} / \mathrm{sec}$
Hence, option ' $b$ ' wave is the maximum wave velocity.