The stationary wave produced on a string is represented by the equation $y = 5 \cos (\pi x / 3) \sin (40 \pi t)$. Where $x$ and $y$ are in $cm$ and $t$ is in seconds. The distance between consecutive nodes is .... $cm$.

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

$A$ stationary wave is represented by $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The distance between two consecutive nodes is (in $cm$)

$A$ stretched string fixed at both ends has $m$ nodes,then the length of the string will be

The ends of a stretched wire of length $L$ are fixed at $x = 0$ and $x = L.$ In one experiment,the displacement of the wire is ${y_1} = A\sin (\pi x/L)\sin \omega t$ and energy is ${E_1}$,and in another experiment its displacement is ${y_2} = A\sin (2\pi x/L)\sin 2\omega t$ and energy is ${E_2}$. Then

The displacement of a string is given by,
$y(x, t) = 10 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$
where $x$ and $y$ are in $m$ and $t$ is in $sec$. The length of the string is $1.5 \ m$ and its mass is $3 \times 10^{-2} \ kg$.
Select the correct statement$(s)$ below:
$(A)$ It represents a progressive wave of frequency $60 \ Hz$.
$(B)$ It represents a standing wave of frequency $60 \ Hz$.
$(C)$ It is the result of two waves of wavelength $3 \ m$,frequency $60 \ Hz$ each travelling with a speed of $180 \ m/s$ in opposite directions.
$(D)$ Reflection occurs from a free end.