$A$ body sends a wave $150 \text{ mm}$ long through medium $P$ and $0.30 \text{ m}$ long in medium $Q$. If velocity of the wave in medium $P$ is $80 \text{ cm s}^{-1}$, the velocity of wave in medium $Q$ is (in $\text{ m s}^{-1}$)

The equation of a travelling wave is $y = a \sin 2 \pi (p t - \frac{x}{5})$. Then the ratio of the maximum particle velocity to the wave velocity 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.

$A$ wave equation which gives the displacement along the $Y$ direction is given by the equation $y = 10^4 \sin(60t + 2x)$,where $x$ and $y$ are in metres and $t$ is time in seconds. This represents a wave:

For the harmonic travelling wave $y = 5 \cos 2\pi (10t - 0.008x + 3.5)$ where $x$ and $y$ are in $cm$ and $t$ is in seconds. What is the phase difference between the oscillatory motion at two points separated by a distance of:
$(a)$ $4 \ m$
$(b)$ $0.5 \ m$
$(c)$ $\frac{\lambda}{2}$
$(d)$ $\frac{3\lambda}{4}$ (at a given instant of time)
$(e)$ What is the phase difference between the oscillation of a particle located at $x = 100 \ cm$,at $t = T \ s$ and $t = 5 \ s$?

$A$ sound of frequency $480 \,Hz$ is emitted from a stringed instrument. The velocity of sound in air is $320 \,m/s$. After completing $180$ vibrations, the distance covered by the wave is: (in $\,m$)