P18_045

# P18_045 - τ ∆ τ and its frequency is f 2 You want to...

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45. Each wire is vibrating in its fundamental mode so the wavelength is twice the length of the wire ( λ =2 L ) and the frequency is f = v/λ =(1 / 2 L ) p τ/µ ,where v (= p τ/µ ) is the wave speed for the wire, τ is the tension in the wire, and µ is the linear mass density of the wire. Suppose the tension in one wire is τ and the oscillation frequency of that wire is f 1 . The tension in the other wire is
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Unformatted text preview: τ + ∆ τ and its frequency is f 2 . You want to calculate ∆ τ/τ for f 1 = 600 Hz and f 2 = 606 Hz. Now, f 1 = (1 / 2 L ) p τ/µ and f 2 = (1 / 2 L ) p ( τ + ∆ τ ) /µ , so f 2 /f 1 = p ( τ + ∆ τ ) /τ = p 1 + (∆ τ/τ ) . This leads to ∆ τ/τ = ( f 2 /f 1 ) 2 − 1 = [(606 Hz) / (600 Hz)] 2 − 1 = 0 . 020 ....
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## This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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