The two waves represented by $y_1 = a \sin(\omega t)$ and $y_2 = b \cos(\omega t)$ have a phase difference of

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

$A$ travelling harmonic wave is represented by the equation $y(x, t) = 10^{-3} \sin(50t + 2x)$,where $x$ and $y$ are in meters and $t$ is in seconds. Which of the following is a correct statement about the wave?

$A$ transverse wave is given by $y = A \sin 2\pi \left( \frac{t}{T} - \frac{x}{\lambda} \right)$. The maximum particle velocity is equal to $4$ times the wave velocity when:

$A$ wave travelling along the $x$-axis is described by the equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and the time period of the wave are $0.08 \ m$ and $2.0 \ s$,respectively,then $\alpha$ and $\beta$ in appropriate units are:

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:
$(a)$ $4 \, m$
$(b)$ $0.5 \, m$
$(c)$ $\lambda / 2$
$(d)$ $3 \lambda / 4$