$A$ standing wave $y = A \sin \left( \frac{20}{3} \pi x \right) \cos (1000 \pi t)$ is maintained in a taut string,where $y$ and $x$ are expressed in meters. The distance between the successive points oscillating with the amplitude $A/2$ across a node is equal to ... $cm$.

The standing wave in a medium is expressed as $y = 0.2 \sin(0.8 x) \cos(3000 t) \, m$. The distance between any two consecutive points of minimum or maximum displacement is

$A$ rod of length $1.2\,m$ is clamped at the midpoint and its fundamental frequency is $2\,MHz$. What is the speed of the wave inside the rod?

Two progressive waves $Y_1 = \sin 2 \pi \left( \frac{t}{0.4} - \frac{x}{4} \right)$ and $Y_2 = \sin 2 \pi \left( \frac{t}{0.4} + \frac{x}{4} \right)$ superpose to form a standing wave. $x$ and $y$ are in $SI$ units. The amplitude of the particle at $x = 0.5 \ m$ is $\left[ \sin 45^{\circ} = \cos 45^{\circ} = \frac{1}{\sqrt{2}} \right]$.

$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

$A$ wave disturbance in a medium is described by $y(x, t) = 0.02 \cos(50 \pi t + \frac{\pi}{2}) \cos(10 \pi x)$,where $x$ and $y$ are in metres and $t$ is in seconds.