Solve explain briefly: Q A suspension bridge is to be built across valley where it is - Physics - Waves

Question

Solve & explain briefly:

Q 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

(1) 2000 m (2) 1000 m
(3) 400 m (4) 80 m

Pintu B. · Accepted Answer

Dear Student ,

Here in this case 5s intervals is a frequency f = 1/T = 1/5 = 0
2Hz
   Since v = fλ, the wavelength for transverse wave on the bridge is given by  400 = 0
2λ  ⇒λ = 2000m   At the fundametal frequency, the bridge's length iequals λ/2 (node to node), so the danger is greatest at , 2000/2 = 1000m
Regards