In stationary waves,

$A$ string of length $0.5 \text{ m}$ and mass $10^{-3} \text{ kg}$ is tightly clamped at its ends. The tension in the string is $0.8 \text{ N}$. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. What is the minimum value of $\Delta t$ which allows constructive interference between successive pulses (in $\text{ s}$)?

What is a refracted wave? $OR$ What is a stationary wave?

The displacement of a string is given by,
$y(x, t) = 10 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$
where $x$ and $y$ are in $m$ and $t$ is in $sec$. The length of the string is $1.5 \ m$ and its mass is $3 \times 10^{-2} \ kg$.
Select the correct statement$(s)$ below:
$(A)$ It represents a progressive wave of frequency $60 \ Hz$.
$(B)$ It represents a standing wave of frequency $60 \ Hz$.
$(C)$ It is the result of two waves of wavelength $3 \ m$,frequency $60 \ Hz$ each travelling with a speed of $180 \ m/s$ in opposite directions.
$(D)$ Reflection occurs from a free end.

$A$ wave $y = a \sin(\omega t - kx)$ on a string meets with another wave producing a node at $x = 0$. Then the equation of the unknown wave is

From the given progressive wave equations,which waves are used to produce a standing wave?
$z_1 = A \cos(\omega t - kx)$
$z_2 = A \cos(\omega t + kx)$
$z_3 = A \cos(\omega t + ky)$
$z_4 = A \cos(2\omega t - 2ky)$