Two waves are represented as $y_1 = a_1 \sin \left( \omega t - \frac{2\pi x}{\lambda} \right)$ and $y_2 = a_2 \cos \left( \omega t - \frac{2\pi x}{\lambda} + \frac{\pi}{6} \right)$. The path difference between the two waves is:

In a plane progressive wave given by $y = 25 \cos (2\pi t - \pi x)$,the amplitude and frequency are respectively

$A$ wave is represented by the equation $y = 7\sin \{ \pi (2t - 2x) \} $ where $x$ is in metres and $t$ is in seconds. The velocity of the wave is ..... $m/s$.

$A$ boat at anchor is rocked by waves whose crests are $100 \,m$ apart and velocity is $25 \,m/s$. The boat bounces up once in every (in $\,s$)

$A$ wave travelling along a string is described by,
$y(x, t) = 0.005 \sin (80.0 x - 3.0 t)$
In which the numerical constants are in $SI$ units ($0.005 \, m, 80.0 \, rad \, m^{-1},$ and $3.0 \, rad \, s^{-1}$). Calculate
$(a)$ the amplitude,
$(b)$ the wavelength,and
$(c)$ the period and frequency of the wave.
Also,calculate the displacement $y$ of the wave at a distance $x = 30.0 \, cm$ and time $t = 20 \, s$.

$A$ wave equation is $y = 10^{-4} \sin(60t + 2x)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. Which of the following statements is correct?