The diagram shows a snapshot of a wave at time $t = 0$. The particle at $x = x_1$ is moving upward at that instant. The direction of propagation of the wave is:

For a wave propagating in a medium, identify the property that is independent of the others.

$A$ travelling wave pulse is given by $y = \frac{4}{3x^2 + 48t^2 + 24xt + 2}$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The velocity of the wave is ........... $m/s$.

$A$ transverse wave on a string is described by $y = 3 \sin(36t + 0.018x + \pi/4)$, where $x$ and $y$ are in $cm$ and $t$ is in seconds. The least distance between two successive crests in the wave is . . . . . . $cm$. (Nearest integer) $(\pi = 3.14)$

In the wave equation $y = 0.5 \sin \frac{2 \pi}{\lambda}(400 t - x ) \, m$,the velocity of the wave will be ......... $m/s$.

$A$ transverse wave propagates in a medium with a velocity of $1450 \, m/s$. The distance between the nearest points at which the oscillations of the particles are in the opposite phase (phase difference of $\pi$) is $0.1 \, m$. What is the frequency of the wave in $Hz$?