The stationary wave $y = 2a \sin kx \cos \omega t$ in a stretched string is the result of the superposition of $y_1 = a \sin(kx - \omega t)$ and

In stationary waves,all particles between two consecutive nodes pass through the mean position:

The correct statement about stationary waves is that

Stationary waves of frequency $300\, Hz$ are formed in a medium in which the velocity of sound is $1200\, m/s$. The distance between a node and the neighbouring antinode is ... $m$.

The following statements are given for a stationary wave:
$(a)$ Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
$(b)$ All the particles cross their mean position at the same time.
$(c)$ All the particles are oscillating with the same amplitude.
$(d)$ There is no net transfer of energy across any plane.
$(e)$ There are some particles which are always at rest.
Which of the following is correct?

$A$ string is rigidly tied at two ends and its equation of vibration is given by $y = \sin(2\pi x) \cos(2\pi t)$. Then the minimum length of the string is .... $m$