If a travelling wave is given by $y(x, t) = 0.5 \sin (70.1 x - 10 \pi t)$,where $x$ and $y$ are in metre,the time $t$ is in second,then the frequency of the wave is (in $Hz$)

For the wave $y(x, t) = 3.0 \sin (36 t + 0.018 x + \pi / 4)$,plot the displacement $(y)$ versus time $(t)$ graphs for $x = 0, 2$ and $4 \; cm$. What are the shapes of these graphs? In which aspects does the oscillatory motion in a travelling wave differ from one point to another: amplitude,frequency,or phase?

The equation of a sound wave is $y = 0.0015 \sin (62.4 x + 316 t)$. Find the wavelength of this wave.

The equation of wave motion is $Y = 6 \sin (12\pi t - 0.02\pi x + \pi/3)$ where $x$ is in metre and time in second. The velocity of the wave is (in $\text{ m/s}$)

The figure represents the instantaneous picture of a transverse harmonic wave traveling along the negative $x$-axis. Choose the correct alternative(s) related to the movement of the points shown in the figure. The points moving with maximum velocity is/are:

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: