Calculating Resonant Frequency of a Bridge with Added Support

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To calculate the new resonant frequency of a bridge with an added support, start by understanding that the natural frequency of the original bridge is 10 Hz. The placement of the support at one-third of the bridge's length alters the harmonic distribution, requiring a new wavelength calculation. The new wavelength with the support is determined to be (2/3)L, where L is the original length of the bridge. By using the relationship between frequency, wavelength, and the speed of waves, the new frequency can be derived and compared to the original 10 Hz. This approach highlights the impact of structural changes on resonant frequencies.
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I am having trouble with the following question:

A bridge has a natural frequence of 10 Hz. If a support is placed one-third of the way along the bridge, what is the new resonant frequency?

How should I start this problem?
 
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When you place a bridge somewhere between the ends, you alter the way the harmonics are distributed.
 
Take "L" to be the length of the original bridge. A wave MUST have a node at the two endpoints where the bridge is fixed so knowing the frequency, you can calculate the wavelength(s) of the resonant frequency in terms of L. If a support is placed at at 1/3 L a resonant frequency must have wave length 2(1/3)L= (2/3)L (2 because there is a node in the middle of a wave length). Calculate the frequency from that (again in terms of L) and compare with the original value.
 

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