The equation of a wave disturbance is given as: $y = 0.02 \cos \left( \frac{\pi}{2} + 50\pi t \right) \cos (10 x),$ where $x$ and $y$ are in meters and $t$ is in seconds. Choose the wrong statement:

What kind of waves can survive as standing waves?

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 ....... $Hz$.

Consider the three waves $z_1, z_2$ and $z_3$ as $z_1 = A \sin(kx - \omega t)$,$z_2 = A \sin(kx + \omega t)$ and $z_3 = A \sin(ky - \omega t)$. Which of the following represents a standing wave?

Stationary waves can be produced in

$A$ suspension bridge is to be built across a valley where it is known that the wind can gust at $5 \,s$ intervals. It is estimated that the speed of transverse waves along the span of the bridge would be $400 \,m/s$. The danger of resonant motions in the bridge at its fundamental frequency would be greater if the span had a length of .......... $m$.