The transverse displacement of a string (clamped at its both ends) is given by $y(x,t) = 0.06 \sin(2\pi x / 3) \cos(120\pi t)$. All the points on the string between two consecutive nodes vibrate with

Which of the following statements is incorrect for a stationary wave?

$A$ stationary wave is formed having $4$ nodes along the $120 \,cm$ length of the string. The wavelength of the wave is (in $\,cm$)

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 .... $cm$.

$A$ standing wave pattern of amplitude $A$ in a string of length $L$ shows $2$ nodes (plus those at two ends). If one end of the string corresponds to the origin and $v$ is the speed of the progressive wave,the disturbance in the string could be represented (with appropriate phase) as:

Standing waves are produced in a $10 \, m$ long stretched string fixed at both ends. If the string vibrates in $5$ segments and the wave velocity is $20 \, m/s$,the frequency is ....... $Hz$.