$A$ wave is given by $y = 3 \sin 2\pi \left( \frac{t}{0.04} - \frac{x}{0.01} \right)$,where $y$ is in $cm$. The frequency of the wave and the maximum acceleration of the particle are:

$A$ sinusoidal wave of wavelength $7.5 \ cm$ travels a distance of $1.2 \ cm$ along the $x$-direction in $0.3 \ s$. The crest $P$ is at $x = 0$ at $t = 0 \ s$ and the maximum displacement of the wave is $2 \ cm$. Which equation correctly represents this wave?

$A$ wave represented by the given equation $Y = A\sin(10\pi x + 15\pi t + \frac{\pi}{3})$,where $x$ is in meters and $t$ is in seconds. The expression represents:

The equation of the wave is $Y = 10 \sin \left(\frac{2 \pi t}{30} + \alpha\right)$. If the displacement is $5 \text{ cm}$ at $t = 0$,then the total phase at $t = 7.5 \text{ s}$ will be (Given: $\sin 30^{\circ} = 0.5$)

$A$ transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \text{ cm/s}$. The wavelength of the wave is $0.5 \text{ m}$ and its amplitude is $10 \text{ cm}$. At a particular time $t$,the snapshot of the wave is shown in the figure. The velocity of point $P$ when its displacement is $5 \text{ cm}$ is:

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.