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 $units$)

The equation of a stationary wave on a string clamped at both ends and vibrating in the third harmonic is $Y = 0.5 \sin(0.314 x) \cos(600 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The length of the vibrating string is: (in $cm$)

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?

In the case of a stationary wave pattern, which of the following statements is $CORRECT$?

$Assertion :$ For the formation of stationary waves,the medium must be bounded having definite boundaries.
$Reason :$ In the stationary wave,some particles of the medium remain permanently at rest.

$A$ 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.)