The equation of a wave is given by $y = 10 \sin \left( \frac{2 \pi}{45} t + \alpha \right)$. If the displacement is $5 \text{ cm}$ at $t = 0$,then the total phase at $t = 7.5 \text{ s}$ is

When two sound waves travel in the same direction in a medium,the displacements of a particle located at $x$ at time $t$ are given by:
$y_1 = 0.05 \cos(0.50 \pi x - 100 \pi t)$
$y_2 = 0.05 \cos(0.46 \pi x - 92 \pi t)$
Then the velocity of the waves is..... $m/s$.

The equation of a simple harmonic wave is given by $y = 3 \sin \frac{\pi}{2}(50t - x)$,where $x$ and $y$ are in metres and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is

$A$ simple harmonic progressive wave is represented by $y = A \sin(120\pi t + 3x)$. The distance between two points on the wave at a phase difference of $\frac{\pi}{3} \text{ radian}$ is

$A$ transverse wave is travelling along a stretched string from right to left. The figure shown represents the shape of the string at a given instant. At this instant,

$A$ traveling wave is described by the equation $y(x,t) = [0.05 \sin(8x - 4t)] \text{ m}$. The velocity of the wave is (All the quantities are in $SI$ units). (in $\text{ m/s}$)