Two waves are represented by the equations $y_1 = a \sin \omega t$ and $y_2 = a \cos \omega t$. The first wave is .....

$A$ 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 $11 \; s$.

$A$ travelling wave in a stretched string is described by the equation $y = A\sin (kx - \omega t)$. The maximum particle velocity is

$A$ transverse wave is described by the equation $y = A \sin [2\pi (f t - x/\lambda ) ]$. The maximum particle velocity is equal to four times the wave velocity if:

When a wave travelling in a medium is reflected from the boundary of a denser medium,which of the following will not change?

Two waves are represented by the equations $y_1 = A \sin (\omega t + kx + 0.57) \ m$ and $y_2 = A \cos (\omega t + kx) \ m$,where $x$ is in metre and $t$ is in second. What is the phase difference between them?