Two simple harmonic progressive waves have displacements $y_1 = a_1 \sin \left(\frac{2 \pi x}{\lambda} - \omega t\right)$ and $y_2 = a_2 \cos \left(\frac{2 \pi x}{\lambda} - \omega t + \phi\right)$. What is the phase difference between the two waves?

The diagram shows a snapshot of a wave at time $t = 0$. The particle at $x = x_1$ is moving upward at that instant. The direction of propagation of the wave is:

Which of the following is different from others?

The equation of a wave motion (with $t$ in seconds and $x$ in metres) is given by $y = 7\sin(7\pi t - 0.4\pi x + \frac{\pi}{3})$. The velocity of the wave will be

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.
$(i) \, y = 5 \cos (4x) \sin (20t)$
$(ii) \, y = 4 \sin (5x - t/2) + 3 \cos (5x - t/2)$
$(iii) \, y = 10 \cos (252\pi t) \cos (250\pi t)$
$(iv) \, y = 100 \cos (100\pi t + 0.5x)$
State which of these represent:
$(a)$ a travelling wave along $-x$ direction
$(b)$ a stationary wave
$(c)$ beats
$(d)$ a travelling wave along $+x$ direction.
Give reasons for your answers.

$A$ wave equation which gives the displacement along the $Y$ direction is given by the equation $y = 10^4 \sin(60t + 2x)$,where $x$ and $y$ are in metres and $t$ is time in seconds. This represents a wave: