$A$ 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 .......... $m$.

$A$ string vibrates according to the equation $y = 5 \sin \left( \frac{2\pi x}{3} \right) \cos (20\pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in $sec$. The distance between two adjacent nodes is .... $cm$.

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.

The correct statement about stationary waves is that

What is the fundamental mode?

Standing waves can be produced: