The equation of a simple harmonic wave is given by $y = 3 \sin \frac{\pi}{2}(50t - x)$,where $x$ and $y$ are in metres and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is

For the travelling harmonic wave $y(x, t) = 2.0 \cos 2 \pi(10 t - 0.0080 x + 0.35)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. Calculate the phase difference between oscillatory motion of two points separated by a distance of:
$(a)$ $4 \, m$
$(b)$ $0.5 \, m$
$(c)$ $\lambda / 2$
$(d)$ $3 \lambda / 4$

When a wave travels in a medium,the particle displacement is given by $y = a \sin(2 \pi (bt - cx))$,where $a, b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

The phase difference between two waves represented by $y_1 = 10^{-6} \sin [100t + (x/50) + 0.5] \, m$ and $y_2 = 10^{-6} \cos [100t + (x/50)] \, m$,where $x$ is expressed in meters and $t$ is expressed in seconds,is approximately .... $rad$.

Select the correct statement about the reflection and refraction of a wave at the interface between medium $1$ and medium $2$.

$A$ 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 $\text{ m s}^{-1}$)