Two waves are approaching each other with a velocity of $20 \ m/s$ and frequency $n$. The distance between two consecutive nodes is

$A$ stationary wave is formed with $3$ nodes along the length of a string of $90 \ cm$. The wavelength of the wave is: (in $cm$)

In a standing wave on a string $:-$

$A$ wave $y = a \cos(kx - \omega t)$ superposes on another wave to form a stationary wave having a node at $x = 0$. What is the equation of the other wave?

If you set up the seventh harmonic on a string fixed at both ends,how many nodes and antinodes are set up in it?

$(i)$ For the wave $y(x, t) = 0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5 \, m$ and its mass is $3.0 \times 10^{-2} \, kg$. Do all the points on the string oscillate with the same $(a)$ frequency,$(b)$ phase,$(c)$ amplitude? Explain your answers.
$(ii)$ What is the amplitude of a point $0.375 \, m$ away from one end?