If the wave equation is $y = 0.08 \sin \frac{2\pi}{\lambda} (200t - x)$,then the velocity of the wave will be:

The wave described by $y = 0.25 \sin(10\pi x - 2\pi t)$,where $x$ and $y$ are in $meters$ and $t$ in $seconds$,is a wave travelling along:

The two waves represented by $y_1 = a \sin(\omega t)$ and $y_2 = b \cos(\omega t)$ have a phase difference of

The equation of a wave is given by $y = 10 \sin \left(\frac{2 \pi t}{30} + \alpha\right)$. If the displacement is $5 \ cm$ at $t = 0 \ s$,then the total phase angle at $t = 7.5 \ s$ will be:

If the equation of a progressive wave is given by $y = 3 \cos \pi (100 t - x) \text{ cm}$,then what is the wavelength of the wave in $\text{cm}$?

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.