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 is:

In a stationary wave,all the particles:

$A$ 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.)

$A$ string fixed at both the ends forms a standing wave with a node separation of $5 \,cm$. If the velocity of the wave on the string is $2 \,m/s$, then the frequency of vibration of the string is (in $\,Hz$)

In stationary waves,antinodes are the points where there is

$A$ string fixed at both ends vibrates in $5$ loops as shown in the figure. The total number of nodes and antinodes respectively are