A suspension bridge is to be built across valley where it is know… - Vidyadip

MCQ

A suspension bridge is to be built across 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
$2000$
✓
$1000$
C
$400$
D
$80$

✓

Answer

Correct option: B.

$1000$

b
(b)

$f=\frac{1}{5}=0.2\,Hz$

$\quad \text { speed }=400\,m / s$

$\lambda=\frac{\text { speed }}{f}=\frac{400}{0.2}=2000\,m .$

for $\frac{\lambda}{2}=L$, resonarce will be greatest. $L=\frac{2000\,m}{2}=1000\,m$.

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