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

$A$ stationary wave is represented by $y = A \sin(100t) \cos(0.01x)$,where $y$ and $A$ are in millimetres,$t$ is in seconds,and $x$ is in metres. The velocity of the constituent wave is ........... $m/s$.

Two waves are approaching each other with a velocity of $20 \ m/s$ and frequency $n$. The distance between two consecutive nodes is

Two progressive waves are travelling towards each other with velocity $50 \,m/s$ and frequency $200 \,Hz$. The distance between two consecutive antinodes is (in $\,m$)

$A$ string is vibrating in its fifth overtone between two rigid supports $2.4 \ m$ apart. The distance between successive node and antinode is (in $m$)

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?