Give the distance between consecutive nodes and antinodes in terms of wavelength $\lambda$.

$A$ wave of frequency $100 \, Hz$ is sent along a string towards a fixed end. When this wave travels back after reflection,a node is formed at a distance of $10 \, cm$ from the fixed end of the string. The speed of the incident (and reflected) wave is .... $m/s$.

Two progressive waves are travelling towards each other with velocity $50 \,m/s$ and frequency $200 \,Hz$. The distance between two consecutive antinodes is (in $\,m$)

$A$ string is vibrating in its fifth overtone between two rigid supports $2.4 \ m$ apart. The distance between successive node and antinode is (in $m$)

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

$(i)$ 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?