Two waves of frequencies $20 Hz$ and $30 Hz$ travel out from a common point. The phase difference between them after $0.6 s$ is:

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.

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

$A$ travelling acoustic wave of frequency $500 Hz$ is moving along the positive $x$-direction with a velocity of $300 ms^{-1}$. The phase difference between two points $x_{1}$ and $x_{2}$ is $60^{\circ}$. The minimum separation between the two points is:

The speed of a wave in a medium is $760\, m/s$. If $3600$ waves are passing through a point in the medium in $2$ minutes, then its wavelength is ...... $m$.

The equation of a wave travelling along the positive $x$-axis,as shown in the figure at $t = 0$,is given by: