Give the values of the amplitude at a node and an anti-node in a stationary wave.

$A$ 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:

$A$ string is vibrating in its fifth overtone between two rigid supports $2.4 \ m$ apart. The distance between successive node and antinode is (in $m$)

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

In a stationary wave,if the distance between a consecutive node and antinode is $5 \ cm$,then find the distance between two consecutive antinodes. (in $cm$)

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