The equation of a stationary wave is $Y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$. The distance between two consecutive nodes in metres is

$A$ standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by $y(x, t) = 0.5 \sin(\frac{5\pi}{4}x) \cos(200\pi t)$. What is the speed of the travelling wave moving in the positive $x$ direction in $m/s$? ($x$ and $t$ are in meter and second,respectively.)

Two travelling waves ${y_1} = A\sin [k(x - ct)]$ and ${y_2} = A\sin [k(x + ct)]$ are superimposed on a string. The distance between adjacent nodes is

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $y = (10 \cos \pi x \sin \frac{2 \pi t}{T}) \, cm$. The amplitude of the particle at $x = \frac{4}{3} \, cm$ will be ........ $cm$.

The equation $y = 0.15 \sin(5x) \cos(300t)$ describes a stationary wave. The wavelength of the stationary wave is .... $m$.

The equation of a stationary wave is $ y = 2 \sin \left( \frac{\pi x}{15} \right) \cos (48 \pi t) $. The distance between a node and its next antinode is (in $units$)