In a stationary wave,if the distance between a consecutive node and antinode is $5 \ cm$,then find the distance between two consecutive antinodes. (in $cm$)

$A$ string fixed at both ends vibrates in a resonant mode with a separation of $2.0 \, cm$ between consecutive nodes. For the next higher resonant frequency,this separation is reduced to $1.6 \, cm$. The length of the string is .... $cm$.

$(i)$ 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?

$A$ sound source of frequency $170 \, Hz$ is placed near a wall. $A$ man walking from the source towards the wall finds that there is a periodic rise and fall of sound intensity. If the speed of sound in air is $340 \, m/s$,the distance (in metres) separating the two adjacent positions of minimum intensity is

The equation $y = 0.15 \sin(5x) \cos(300t)$ describes a stationary wave. The wavelength of the stationary wave is .... $m$.

The figure shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ among $1, 2,$ and $3$ are in phase with point $X$?