$A$ 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 .... $m$

$A$ wave travelling along a uniform string represented by $Y=A \sin (\omega t-k x)$ is superimposed on another wave travelling along the same string represented by $Y=A \sin (\omega t+k x)$. The resultant is

For a stationary wave represented by the equation $y = 0.15 \sin(5x) \cos(300t) \, \text{m}$,what is the wavelength of the wave (in $, \text{m}$)?

$A$ stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is '$x$'. The length of the string in terms of the wavelength of waves formed in it is $(\lambda = \text{wavelength})$

$A$ wave represented by the equation $y_1 = a \cos(kx - \omega t)$ is superimposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation for the other wave is

$A$ 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.)