The displacement $y$ (in $cm$) in case of a simple harmonic wave is given by $y=\frac{10}{\pi} \sin \left(2000 \pi t-\frac{\pi x}{17}\right)$. The period and maximum velocity of the particles in the medium will respectively be

$A$ travelling harmonic wave on a string is described by $y(x, t) = 7.5 \sin (0.0050 x + 12 t + \pi / 4)$.
$(a)$ What are the displacement and velocity of oscillation of a point at $x = 1 \; cm$ and $t = 1 \; s$? Is this velocity equal to the velocity of wave propagation?
$(b)$ Locate the points of the string which have the same transverse displacements and velocity as the $x = 1 \; cm$ point at $t = 2 \; s, 5 \; s$ and $11 \; s$.

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

The equation of a longitudinal wave is represented as $y = 20 \cos \pi (50t - x)$. Its wavelength is ..... $cm$.

For a transverse wave travelling along a straight line,the distance between two peaks (crests) is $5 \, m$,while the distance between one crest and one trough is $1.5 \, m$. The possible wavelengths (in $m$) of the waves are

The figure shows a sinusoidal wave at a given instant. Which points are in the same phase?