Question

13. 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​

Answer 1

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

ans is 1000m

Answer 2

Answer:

for stationary waves formula of funda mental frequency is f = v/2l

given values are f= 1/5 , v= 400 m/s ,

so by formula,. 1/5 = 400/2l

we get l= 1000m... our req.. correct answer