For waves propagating in a medium,identify the property that is independent of the others.

$A$ 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 progressive wave is $y = 4 \sin(4 \pi t - 0.04 x + \pi / 3)$, where $x$ is in meters and $t$ is in seconds. The velocity of the wave is:

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

$A$ 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?

$A$ transverse sinusoidal wave of amplitude '$a$',wavelength $\lambda$,and frequency $f$ is travelling on a stretched string. The maximum speed at any point on the string is $v/10$,where $v$ is the speed of propagation of the wave. If $a = 10^{-3} \ m$ and $v = 10 \ ms^{-1}$,then $\lambda$ and $f$ are given by: