$A$ stationary wave is formed with $3$ nodes along the length of a string of $90 \ cm$. The wavelength of the wave is: (in $cm$)

Consider the three waves $z_1, z_2$ and $z_3$ as $z_1 = A \sin(kx - \omega t)$,$z_2 = A \sin(kx + \omega t)$ and $z_3 = A \sin(ky - \omega t)$. Which of the following represents a standing wave?

$A$ standing wave pattern is formed on a string. One of the waves is given by the equation $y_1 = a \cos(\omega t - kx + \pi/3)$. Find the equation of the other wave such that at $x = 0$,a node is formed.

$A$ string of mass $0.1 \ kg \ m^{-1}$ has length $0.9 \ m$. It is fixed at both ends and stretched such that it has a tension of $40 \ N$. The string vibrates in three segments with amplitude $0.3 \ cm$. The amplitude (maximum) of the particle velocity is (in $m/s$):

The transverse displacement of a string clamped at its both ends is given by $y(x, t) = 2 \sin \left( \frac{2\pi}{3} x \right) \cos (100 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. Which of the following statements is correct?

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).