Consider the snapshot of a wave traveling in the positive $x$-direction.

The equations of two simple harmonic waves are given by $Y_1 = 2 \sin 8 \pi \left(\frac{t}{0.2} - \frac{x}{2}\right) \text{ m}$ and $Y_2 = 4 \sin 8 \pi \left(\frac{t}{0.16} - \frac{x}{1.6}\right) \text{ m}$. Then both waves have:

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.
$(i) \, y = 5 \cos (4x) \sin (20t)$
$(ii) \, y = 4 \sin (5x - t/2) + 3 \cos (5x - t/2)$
$(iii) \, y = 10 \cos (252\pi t) \cos (250\pi t)$
$(iv) \, y = 100 \cos (100\pi t + 0.5x)$
State which of these represent:
$(a)$ a travelling wave along $-x$ direction
$(b)$ a stationary wave
$(c)$ beats
$(d)$ a travelling wave along $+x$ direction.
Give reasons for your answers.

The equation of a wave is $y = 60 \sin (1200 t - 6 x)$,where '$y$' is in micron,'$t$' is in second,and '$x$' is in metre. The ratio of the maximum particle velocity to the wave velocity of wave propagation is:

The equation of a transverse wave travelling along a string is $y(x, t) = 4.0 \sin(20 \times 10^{-3} x + 600 t) \ mm$,where $x$ is in $mm$ and $t$ is in seconds. The velocity of the wave is:

The amplitude of a wave disturbance propagating in the positive $X-$ direction is given by $y = 1/(1 + x^2)$ at time $t = 0$ and by $y = 1/[1 + (x - 1)^2]$ at $t = 2$ seconds,where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ..... $ms^{-1}$.