The correct statement about stationary waves is that

The $(x, y)$ coordinates of the corners of a square plate are $(0, 0), (L, 0), (L, L)$ and $(0, L).$ The edges of the plate are clamped and transverse standing waves are set up in it. If $u(x, y)$ denotes the displacement of the plate at the point $(x, y)$ at some instant of time,the possible expression$(s)$ for $u$ is(are) ($a =$ positive constant).

$A$ wave $y = a \cos (kx + \omega t)$ superimposes on another wave to form a stationary wave having a node at $x = 0$. What is the equation of the other wave?

The transverse displacement of a string of a linear density $0.01 \text{ kg m}^{-1}$,clamped at its ends is given by $Y_{(x, t)} = 0.03 \sin \left(\frac{2 \pi x}{3}\right) \cos (60 \pi t)$,where $x$ and $y$ are in metres and time $t$ is in seconds. The tension in the string is: (in $\text{ N}$)

$A$ string is rigidly tied at two ends and its equation of vibration is given by $y = \sin(2\pi x) \cos(2\pi t)$. Then the minimum length of the string is .... $m$

The given diagram shows a detector placed between a transmitter of sound waves and a metal plate. At three adjacent points,$R, S$ and $T$,the meter shows zero intensity. Which of the following is the frequency of the emitted wave in $Hz$? (Take the velocity of sound as $v = 300 \, m/s$)