The expression $y = a \sin bx \sin \omega t$ represents a stationary wave. The distance between the consecutive nodes is equal to

$A$ pulse or a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with

Two progressive waves $Y_1 = \sin 2 \pi \left( \frac{t}{0.4} - \frac{x}{4} \right)$ and $Y_2 = \sin 2 \pi \left( \frac{t}{0.4} + \frac{x}{4} \right)$ superpose to form a standing wave. $x$ and $y$ are in $SI$ units. The amplitude of the particle at $x = 0.5 \ m$ is $\left[ \sin 45^{\circ} = \cos 45^{\circ} = \frac{1}{\sqrt{2}} \right]$.

$A$ stationary wave is represented by $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The distance between two consecutive nodes is (in $cm$)

Two waves of same frequency $(n)$ are approaching each other with same velocity of $12 \ m/s$ along the same linear path and interfere. The distance between two consecutive nodes is

Which of the following statements is incorrect for a stationary wave?